Question

A computer disk drive is turned on starting from rest and has constant angular acceleration.

Part A

If it took 0.420 s for the drive to make its second complete revolution, how long did it take to make the first complete revolution?

Part B

What is its angular acceleration, in rad/s²?

Answer 1

Part A

Using second rotational kinematic law,

= wi*t + 0.5*alpha*t^2

here, wi = initial angular speed = 0

for the drive to make its second complete revolution,

2 = 2 rev = 2*2*pi rad

t2 = 0.420 s

now, for the drive to make its first complete revolution,

1 = 1 rev = 1*2*pi rad

t1 = ??

So, 1/2 = (wi*t1 + 0.5*alpha*t1^2)/(wi*t2 + 0.5*alpha*t2^2)

Using known values:

(1*2*pi)/(2*2*pi) = (0 + 0.5*alpha*t1^2)/(0 + 0.5*alpha*t2^2)

1/2 = t1^2/t2^2

t1 = sqrt(t2^2/2) = sqrt(0.420^2/2)

t1 = 0.297 s

Part B

Now, again using second rotational kinematic law for second complete revolution,

2 = wi*t2 + 0.5*alpha*t2^2

alpha = angular acceleration = 2*2/t2^2

alpha = 2*(2*2*pi)/(0.420^2)

alpha = 142.5 rad/s^2