Week 2 Query

#$&*

course Mth 164

If your solution to stated problem does not match the given solution, you should self-critique per instructions at

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm

.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

&&&& query modeling exercise

&&&& What is the distance between the peaks of the graph for which the angular velocity of the reference point is 3 rad / sec, and what are the maximum and minimum vertical coordinates if the circle is centered at vertical coordinate 12?

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Your solution:

I’m not sure I understand the question.

???Are we saying that period T is 3 rad / sec.

@& The period is not measured in radians per second. The angular velocity of the point on the reference circle is 3 radians / second.

Think of the ant on the circle. The radial line, from the center of the circle to the ant, makes and angle with the positive x axis. This angle is changing at 3 radians / second.************

****************@

??? How can we figure the max. and min. vertical coordinates if we are not given a radius dimension.

I know that from one maximum peak to the next maximum peak is the same as one revolution.

@& The modeling exercise you did (or should have done) prior to starting this query did specify a radius. That exercise should have been worked out on paper.*@

Ok, I thought I was missing some pertinent information and this ended up being the case.

I checked ahead at the class lectures listed for assignment 2 and they refer to these questions.

@& Ok, now you're on track.

Just to be sure:

The last thing you do in an assignment is the Query. All other parts of the assignment should be done first.*@

Attempt #2

If the radius is 5, and the vertical coordinate 12 is the center of the circle, the minimum vertical coordinate is 12 - 5 = 7 and the maximum vertical coordinate is 12 + 5 = 17.

In this question we are looking for period T. Period T is the same distance as the circumference of a circle. Period T = 2pi radians.

@& The period isn't 2 pi radians, the angular displacement around the circle is 2 pi radians. It seems clear from what follows that you understand this.*@

We are moving at a rate of 3 rad / sec. We know that a circle is approximately 6.28 radians. To get the exact distance with respect to time(omega), we do as follows:

period T = 2pi rad/(3 rad/sec) = 2pi/3 sec or approx. 2.09 sec

confidence rating #$&*: 3

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Given Solution:

** At 3 rad/sec a complete trip around the reference circle takes 2 pi / 3 seconds, close to but not exactly 2 seconds. 2 pi / 3 seconds is the distance between the peaks on the graph of y vs. t.

If the circle has radius 5 the max and min will be 5 units above and below the center of the circle, at 12 - 5 = 7 and 12 + 5 = 17. **

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15:10:20

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Self-critique (if necessary):

After studying the given solution, I am still confused.

Critique #2:

@& Your solution, which you're explained well, seems to be very consistent with the given solution.*@

OK

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Self-critique Rating: 3

&&&& Given the values between which a cyclical quantity varies, how you determine where to position the circle that models the quantity, and how the determine the radius of the circle?

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15:22:13

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Your solution:

We position the circle with the center halfway between minimum and maximum values. We find the center by adding the min and max values and dividing by two to get the average. The radius can be found by finding the difference of the min and max and dividing difference by 2.

confidence rating #$&*: 3

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Given Solution:

** The center of the circle will be halfway between the max and min values, which can be found by averaging the two values (i.e., add and divide by 2).

The diameter will be the difference between the max and min values and the radius will be half of the diameter. **

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15:22:16

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

&&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the daylight model?

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Your solution:

If we compare a day to a circle, it takes 24 hrs to complete one revolution. Therefore we have:

angular speed = 1 rev / 24 hrs * 2pi rad / rev = 2pi/24 rad/hrs = pi/12 rad/hrs or pi/12 hrs

The difference from one day to the next is 24 hrs. Therefore 24/2 is the vertical coordinate, which is 12.

Attempt#2:

If the cycle equals 1 year and the length of a day varies from 9 hrs to 15 hrs over this period we can model this data on a graph of y vs t.

omega = theta / t

omega = (2 pi rad)/ 12 months = pi/6 rad/month

If we let y = the number of hrs then the center of the circle would be (9 + 15) / 2 = 12 = y

confidence rating #$&*: 3

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Given Solution:

** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week.

If the period is in months then you have 2 pi / 12 cycles per month, or pi/6 cycles per month.

The vertical coordinate of the center will be the day length midway between the min and max day lengths, which is 12 hours.**

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Self-critique (if necessary):

I’m not sure if I understand the jargon being used.

???Is a cycle the distance, with respect to time, between peaks(period T) on the graph y vs t and the wavelength on the graph y vs x.

Disregard this self critique…

@& Just to be clear, a cycle corresponds to one complete circuit around the reference circle.

And from peak to peak on the graph corresponds to a complete circuit around the reference.

So I think you've got it.*@

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Self-critique Rating: 3

&&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the temperature model?......!!!!!!!!...................................

15:55:04

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Your solution:

I don’t think I understand the question. If the temperature ranged from 0 to 100 degrees in one cycle, then the center of the circle would be the difference divided by 2. In this case, the vertical coordinate would be 50.

Attempt#2:

If in one a 1 day cycle the temperature varies from 5 to 39 degrees over this period we can model this data on a graph of y vs t.

One day is one cycle. Therefore, 2pi rad/day is the angular speed. The center of the graph would on the line y = (5 + 39)/2 = 22.

confidence rating #$&*: 3

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Given Solution:

** If the period is 52 weeks then you have 2 pi / 52 cycles in a week or pi/26 cycles per week.

The vertical coordinate of the center will be the temperature midway between the min and max temperatures.**

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15:58:33

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Self-critique (if necessary):

???I don’t understand what angular velocity of the reference point means.

Disregard this self critique…

@& In the first example, that would be the 3 radians / second.

In this example that is 2 pi radians / (52 weeks) = pi / 26 rad / week.*@

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Self-critique Rating: 3

&&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the tide model?

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Your solution:

If it takes 20 hrs for the tide to complete 2 cycles, we have:

omega = (2 rev/20 hrs) = (2 rev/20hrs)*(2pi rad/rev) = 4pi/20 rad/hrs = pi/5 rad/hr

The mid point between the low and high tides would serve as the center of the graph.

confidence rating #$&*: 3

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Given Solution:

** If you have a cycle in 10 hours then you have 2 pi rad in 10 hours, or 2 pi / 10 = pi/5 rad / hour.

The vertical coordinate of the center will be the water level midway between the min and max water levels. **

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15:58:35

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

&&&& What is the vertical coordinate of the center of the circle, and what is the angular velocity of the reference point, for the ocean wave model?

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Your solution:

This question depends on whether you are modeling 1 wave or several.

The model for 1 wave could start at the minimum water height and end at a value equal to this. In this case, the angular speed would 2pi r/some unit of time.

If we are modeling the wave height over several cycles then we would measure the height of each wave and this would determine the minimum and maximum values to be used in the model. In this case, the center of the circle is located midway between the minimum and maximum wave height.

confidence rating #$&*: 3

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Given Solution:

** The center will lie halfway between the highest and lowest levels.

At 5 waves per minute the angular frequency would be 5 periods / minute * 2 pi rad / period = 10 pi rad / min. **

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Self-critique (if necessary):

OK

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Self-critique Rating:

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

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Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

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YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

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YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

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YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

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Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

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Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

&&&& query ch. 5 # 78 15 in wheels at 3 rev/sec. Speed in in/s and mph: rpm?

......!!!!!!!!...................................

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

The radius of the wheels for this question is 15 in.

If the wheels making 3 revolutions per second, we can find the angular speed as follows:

omega = angular speed

omega = 3 rev/sec = (3 rev/sec)*(2pi rad/rev) = 6pi /sec

v = linear speed = r * omega

v = 15 in * 6pi rad/sec = 90pi in/sec or approx. 283 in/sec

v = (90pi in/sec) * (mi/63360 in) * (3600 sec/hr) = 324000pi/63360 mi/hr or approx. 16.1 mi/hr

Another way to approach this question is to note that 1 revolution of the wheel occurs every 1/3 second. C = 2pi r; where r is radius and C is circumference.

Using the formula we have:

C=2pi*15 inches

C=30pi inches

30pi inches/(1/3 second) = 90pi inches/second

confidence rating #$&*: 3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.............................................

Given Solution:

** If 15 inches is the diameter of the wheel then the radius is 15 inches.

The angular velocity is 3 rev / sec * 2 pi rad / rev = 6 pi rad / sec.

Each radian of angular displacement corresponds to a distance along the arc which is equal to the radius. So

6 pi rad / sec * 15 inches / radian = 90 pi inches / second.

If you approximate this you get around 280 in/sec.

This is 280 in / sec * 1 ft / 12 in = 23 ft / sec approx.

A mile is 5280 ft and an hour is 3600 sec so this is

23 ft/sec * 1 mile / 5280 ft * 3600 sec / 1 hr. = 16 miles / hr approx.. **

Note that 3 revolutions / second is 180 revolutions / minute, since there are 60 seconds in a minute.

.........................................

&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

Self-critique (if necessary):

OK

------------------------------------------------

Self-critique Rating: OK

#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!#*&!

@& Very good. You really got this on your own and probably don't need the notes I've inserted, but check them out anyway, for reinforcement if nothing else.*@