Practice 7C: | 1 | 2 |
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**Angular Acceleration - by Matt Henderson, 2003**

**1. A figure skater begins spinning counterclockwise at an
angular speed of 4.0**p**
rad/s. During a 3.0 s interval, she slowly pulls her
arms inward and finally spins at 8.0**p**
rad/s. What is her average acceleration
during this time interval?**

Here's what you know, w

_{i}= 4.0p rad/s and w_{f }= 8.0p rad/s and t = 3.0 s use the formula a_{avg}= Dw/Dt to find the average acceleration. Plug it in a_{avg}= (8.0p-4p)/3.0 = 4.2 rad/s^2

**2. What angular acceleration is necessary to increase the
angular speed of a fan blade form 8.5 rad/s to 15.4 rad/s in 5.2 s?**

Here's what you know, w

_{i}= 8.5 rad/s and w_{f }= 15.4 rad/s and t = 5.2 s use the formula a_{avg}= Dw/Dt to find the average acceleration. Plug it in a_{avg}= (15.4-8.5)/5.2 = 1.327 rad/s^2

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**3. Fill in the unknown quantities in the following table:**

a

_{avg}Dw Dta. ? 121.5 rad 7 s

b. .75 rev/s^2 ? .050 s

c. ? -1.2 turns 1.2 s

a. plug the numbers into the formula a

_{avg}= Dw/Dt so a_{avg}= 2.3/10 = 17 rad/s^2b.plug the numbers into the formula a

_{avg}= Dw/Dt to find the change in acceleration so .75 = Dw/.05 = 0.038 rad/sc. since -1.2 turn/s = -1.2 rev/s and we know 1 rev/s = 2p so we multiply -1.2 by 2 pie which equals -7.5398 rad/s

Now plug the numbers into the formula a

_{avg}= Dw/Dt so a_{avg}= -7.5398/1.2 = -6.3 rad/s^2

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