Practice 7C: | 1 | 2 | 3 |Go up
Angular Acceleration  - by Matt Henderson, 2003

1. A figure skater begins spinning counterclockwise at an angular speed of 4.0p rad/s. During a 3.0 s interval, she slowly pulls her arms inward and finally spins at 8.0p 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 

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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                                                    Dt

a.     ?                                            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^2

b.plug the numbers into the formula a_avg = Dw/Dt  to find the change in acceleration so .75 = Dw/.05 = 0.038 rad/s

c. 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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