course Phy 201 `questionNumber 290000 `q001. Note that this assignment contains 15 questions.
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RESPONSE --> Well, since the radius is 40 meters, then one radian would be 40 meters. 3 radians would be 3*40 m=120 m confidence assessment: 3
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14:58:59 `questionNumber 290000 Since 1 radian of angle corresponds to the distance along the arc which is equal to the radius, if the radius of the circle is 40 meters then a 1 radian angle would correspond to a distance of 40 meters along the arc. An angle of 3 radians would correspond to a distance of 3 * 40 meters = 120 meters along the arc. Each radian corresponds to a distance of 40 meters along the arc.
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RESPONSE --> This stuff is actually quite familiar to me... a nice change! self critique assessment: 3
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15:04:40 `questionNumber 290000 `q002. On a circle of radius 40 meters, how far would you have to walk to go all the way around the circle, and through how many radians of angle would you therefore travel? Through how many radians would you travel if you walked halfway around the circle? Through how many radians would you travel if you walked a quarter of the way around the circle?
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RESPONSE --> I guess I should use the circumference formula: C=2pi*r =2(3.14)(40m) =251.2m I am not sure how to answer the rest of the question. confidence assessment: 2
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15:06:52 `questionNumber 290000 The circumference of a circle is the product of `pi and its diameter, or in terms of the radius r, which is half the diameter, C = 2 `pi r. The circumference of this circle is therefore 2 `pi * 40 meters = 80 `pi meters. This distance can be left in this form, which is exact, or if appropriate this distance can be approximated as 80 * 3.14 meters = 251 meters (approx). The exact distance 2 `pi * 40 meters is 2 `pi times the radius of the circle, so it corresponds to 2 `pi radians of arc. Half the arc of the circle would correspond to a distance of half the circumference, or to 1/2 ( 80 `pi meters) = 40 `pi meters. This is `pi times the radius so corresponds to `pi radians of angle. A quarter of an arc would correspond to half the preceding angle, or `pi/2 radians.
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RESPONSE --> I see--instead of obtaining aliteral answer I should have left the answer in exact form as 2pi(40m). Since this is the circumference formula, we know that the 2 pi in front of 40 means the entire circle is 2 pi radians. Half the circle would merely be half of teh entire circumference, or one pi. One fourth of the arc would be the half divided by two again, so pi/2 radians. self critique assessment: 2
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15:11:57 `questionNumber 290000 `q003. On a circle of radius 6 meters, what distance along the arc would correspond to 3 radians? What distance would correspond to `pi / 6 radians? What distance would correspond to 4 `pi / 3 radians?
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RESPONSE --> 3 * 6m (radius length)=18 m pi/6*6 cancels the 6's, leaving only pi for the second part of the question. (4(pi/3)) * 6 = 24 pi/3=8 pi m confidence assessment: 3
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15:12:12 `questionNumber 290000 3 radians along the arc would correspond to an arc distance of 3 times the radius, or 3 * 6 meters, or 18 meters. `pi / 6 radians would correspond to `pi / 6 times the radius, or `pi / 6 * 6 meters = `pi meters. 4 `pi / 3 radians would correspond to 4 `pi / 3 * 6 meters = 8 `pi meters.
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RESPONSE --> I understand. So far this stuff is rather simple. self critique assessment: 3
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15:13:22 `questionNumber 290000 `q004. If you were traveling around a circle of radius 50 meters, and if you traveled through 4 radians in 8 seconds, then how fast would you have to be moving?
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RESPONSE --> 4 * 50m=200 m 200m/8 seconds=25 m/s confidence assessment: 3
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15:13:29 `questionNumber 290000 If you travel 4 radians along the arc you half traveled an arc distance of 4 times the radius, or 4 * 50 meters = 200 meters. If you traveled this distance in 8 seconds your average speed would be 200 meters / (8 seconds) = 25 m/s.
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RESPONSE --> I understand. self critique assessment: 3
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15:14:26 `questionNumber 290000 `q005. Traveling at 3 radians / second around a circle of radius 20 meters, how fast would you have to be moving?
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RESPONSE --> 3 *20 m=60 m 60m/s confidence assessment: 3
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15:14:33 `questionNumber 290000 3 radians along the arc is a distance of 3 times the radius, or 3 * 20 meters = 60 meters. Moving at 3 radians/second, then, the speed along the arc must be 3 * 20 meters / sec = 60 meters /sec.
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RESPONSE --> I understand. self critique assessment: 4
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15:15:36 `questionNumber 290000 `q006. If you know how many radians an object travels along the arc of a circle, and if you know the radius of the circle, how do you find the distance traveled along the arc? Explain the entire reasoning process.
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RESPONSE --> The number of radians multiplied by the radius distance gives the arc distance. confidence assessment: 2
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15:15:45 `questionNumber 290000 The distance traveled along the arc of circle is 1 radius for every radian. Therefore we multiply the number of radians by the radius of the circle to get the arc distance.
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RESPONSE --> I understand. self critique assessment: 3
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15:16:59 `questionNumber 290000 `q007. If you know the distance an object travels along the arc of a circle, and if you know the radius of the circle, how do you find the corresponding number of radians?
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RESPONSE --> One can divide the distance by the radius length to get the number of radians. confidence assessment: 3
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15:17:12 `questionNumber 290000 An arc distance which is equal to the radius corresponds to a radian. Therefore if we divide the arc distance by the radius we obtain the number of radians.
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RESPONSE --> I understand. self critique assessment: 3
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15:18:57 `questionNumber 290000 `q008. If you know the time required for an object to travel a given number of radians along the arc of a circle of known radius, then how do you find the average speed of the object?
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RESPONSE --> First one has to multiply the number or radians by the radius lenght to get the distance. Then, one divides the distances traveled by the time to obtain the average speed. confidence assessment: 3
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15:19:10 `questionNumber 290000 If you know the number of radians you can multiply the number of radians by the radius to get the distance traveled along the arc. Dividing this distance traveled along the arc by the time required gives the average speed of the object traveling along the arc.
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RESPONSE --> I understand. self critique assessment: 3
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16:15:27 `questionNumber 290000 `q009. If you know the speed of an object along the arc of a circle and you know the radius of the circle, how do you find the angular speed of the object in radians/second?
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RESPONSE --> not sure... confidence assessment: 0
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16:16:34 `questionNumber 290000 The speed of the object is the distance it travels along the arc per unit of time. The angular velocity is the number of radians through which the object travels per unit of time. The distance traveled and the number radians are related by the fact that the distance is equal to the number of radians multiplied by the radius. So if the distance traveled in a unit of time is divided by the radius, we get the number of radians in a unit of time. So the angular speed is found by dividing the speed along the arc by the radius.
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RESPONSE --> I see that the difference between average speed and angular velocity is that angular velocity is radians/time instead of distance/time. self critique assessment: 2
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16:20:41 `questionNumber 290000 `q010. We usually let `d`theta stand for the anglular displacement in radians between two points on the arc of the circle. We usually let `omega stand for the angular velocity in radians / second. We let `ds stand for the distance traveled along the arc of a circle, and we let r stand for the radius of the circle. If we know the radius r and the arc distance `ds, what is the anglular displacement `d`theta, in radians?
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RESPONSE --> 'd'theta='ds/r confidence assessment: 1
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16:21:02 `questionNumber 290000 Since an angular displacement of 1 radian corresponds to an arc distance equal to the radius, the anglular displacement `theta in radians is equal to the number of radii in the arc distance `ds. This quantity is easily found by dividing the arc distance by the radius. Thus `d`theta = `ds / r.
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RESPONSE --> I just sorta made my best guess and got it right, but I do understand how this formula is derived now. self critique assessment: 2
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16:26:11 `questionNumber 290000 `q011. If we know the radius r of a circle and the angular velocity `omega, how do we find the velocity v of the object as it moves around the arc of the circle?
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RESPONSE --> v='omega*r 'omega is radians/second. Since 1 radian=1 unit of radius, when we multiply these we get the distance/second. I think of it as v=(radians/second)*(radius) =radians*radius/second='distance/second=velocity confidence assessment: 2
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16:26:18 `questionNumber 290000 The angular velocity is the number of radians per second. The velocity is the distance traveled per second along the arc. Since an angular displacement of 1 radian corresponds to an arc distance equal to the radius, if we multiply the number of radians per second by the radius we get the distance traveled per second. Thus v = `omega * r.
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RESPONSE --> I understand. self critique assessment: 3
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16:35:03 `questionNumber 290000 `q012. We can change an angle in degrees to radians, or vice versa, by recalling that a complete circle consists of 360 degrees or 2 `pi radians. A half-circle is 180 degrees or `pi radians, so 180 degrees = `pi radians. How many radians does it take to make 30 degrees, how many to make 45 degrees, and how many to make 60 degrees?
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RESPONSE --> 30/180=1/6 pi/6 45/180=1/4 pi/4 60/180=1/3 pi/3 confidence assessment: 3
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16:35:14 `questionNumber 290000 30 degrees is 1/6 of 180 degrees and therefore corresponds to 1/6 * `pi radians, usually written as `pi/6 radians. 45 degrees is 1/4 of 180 degrees and therefore corresponds to 1/4 * `pi radians, or `pi/4 radians. 60 degrees is 1/3 of 180 degrees and therefore corresponds to 1/3 * `pi radians, or `pi/3 radians.
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RESPONSE --> I remember all this stuff from trig thankfully./ self critique assessment: 3
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16:37:15 `questionNumber 290000 `q013. Since 180 deg = `pi rad, we can convert an angle from degrees to radians or vice versa if we multiply the angle by either `pi rad / (180 deg) or by 180 deg / (`pi rad). Use this idea to formally convert 30 deg, 45 deg and 60 deg to radians.
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RESPONSE --> 30 degrees 30*(pi/180)=pi/6 radians 45 degrees 45*(pi/180)=pi/4 60 degrees 60*(pi/180)=pi/3 confidence assessment: 3
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16:37:22 `questionNumber 290000 To convert 30 degrees to radians, we multiply by the rad / deg conversion factor, obtaining 30 deg * ( `pi rad / 180 deg) = (30 deg / (180 deg) ) * `pi rad = 1/6 * `pi rad = pi/6 rad. To convert 45 degrees to radians we use the same strategy: {}45 deg * (`pi rad / 180 deg) = ( 45 deg / ( 180 deg) ) * `pi rad = 1/4 * `pi rad = `pi/4 rad. To convert 60 degrees: 60 deg * (`pi rad / 180 deg) = ( 60 deg / ( 180 deg) ) * `pi rad = 1/3 * `pi rad = `pi/3 rad.
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RESPONSE --> I understand. self critique assessment: 3
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16:39:47 `questionNumber 290000 `q014. Convert 50 deg and 78 deg to radians.
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RESPONSE --> 50 degrees 50*(pi/180) 50pi/180=5pi/18 78 degrees 78pi/180 13pi/30 I don't know if these can be simplified or if they should be simplified more. confidence assessment: 2
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16:39:52 06-25-2007 16:39:52 50 deg * (`pi rad / 180 deg) = ( 50 deg / ( 180 deg) ) * `pi rad = 5/18 * `pi rad = (5 `pi/ 18) rad. 78 deg * (`pi rad / 180 deg) = ( 78 deg / ( 180 deg) ) * `pi rad = 78/180 * `pi rad = (13 `pi/ 30) rad.
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16:41:41 `questionNumber 290000 `q015. Convert (14 `pi / 9) rad to degrees.
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RESPONSE --> 14pi/9 * (180/pi) the pi's cancel 14*180/9= 2520/9= 280 confidence assessment: 3
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16:41:51 `questionNumber 290000 Since the angle is given radians, we need to multiply by deg / rad to get the angle in degrees. (14 `pi / 9) rad * ( 180 deg / (`pi rad)) = ( 14 `pi / 9 ) * (180 / `pi ) deg = ( 14 * 180 / 9) * (`pi / `pi) deg = 14 * 20 deg = 280 deg.
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RESPONSE --> I understand. self critique assessment: 3
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