assn 30 1

course phys201

First part of assn 30

confidence assessment: 3

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12:48:38

Starting at 3 rad/s and ending up at 8 rad/s, the average angular velocity would be expected to be greater than the minimum 3 rad/s and less than the maximum 8 rad/s. If the angular velocity changes at a constant rate, we would in fact expect the average angular velocity to lie halfway between 3 rad/s and 8 rad/s, at the average value (8 rad/s + 3 rad/s) / 2 = 5.5 rad/s.

Moving at this average angular velocity for 10 sec the object would rotate through 5.5 rad/s * 10 s = 55 rad in 10 sec.

The change in the angular velocity during this 10 seconds is (8 rad/s - 3 rad/s) = 5 rad/s; this change takes place in 10 seconds so that the average rate at which the angular velocity changes must be ( 5 rad / sec ) / (10 sec) = .5 rad/s^2. This is called the average angular acceleration.

Angular acceleration is designated by the symbol `alpha. Since the angular velocity in this example changes at a constant rate, the angular acceleration is constant and we therefore say that

`alpha = `d `omega / `dt.

Again in this case `d`omega is the 5 rad/sec change in the angular velocity.

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RESPONSE -->

self critique assessment: 3

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12:50:06

`q004. If an object starts out with angular velocity 14 rad/s and accelerates at a rate of 4 rad/s^2 for 5 seconds, then at what rate is the object rotating after the 5 seconds? Through how many radians will the object rotate during this time?

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RESPONSE -->

4 rad/s * 5 = 20 rad/s

20 rad/s + 14 rad/s = 34 rad/s

14 rad/s + 34 rad/s / 2 = 24 rad/s.

24 rad/s * 5 sec = 120 rad

confidence assessment: 3

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12:50:45

Changing angular velocity at the rate of 4 rad/s^2 for 5 sec the angular velocity will change by (4 rad/s^2) (5s) = 20 rad/s.

Since the angular velocity was already 14 rad/s at the beginning of this time period, it will be 14 rad/s + 20 rad/s = 34 rad/s at the end of the time period.

The uniform rate of change of angular velocity implies that the average angular velocity is (14 rad/s + 34 rad/s) / 2 = 24 rad/s.

An average angular velocity of 24 radians/second, in 5 seconds the object will rotate through an angle `d`theta = (24 rad/s) ( 5 sec) = 120 rad.

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RESPONSE -->

self critique assessment: 3

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