Question

A disk spinning at an initial angular velocity ω decelerates at a constant rate α until it comes to a stop after a time t. If its inital angular velocity is doubled but all else remains the same, how long will it take to stop?

21/2 t
	4t
	t
	2t

Answer 1

initial angular velcity = $\omega$

deceleration = $\alpha$

Final angular velocity = 0

$0 = \omega - \alpha t$

=> t = $\frac{\omega }{\alpha }$

Case 2

Initial angluar velocity = $2\omega$

deceleration = $\alpha$

Final angular velocity = 0

$0 = 2\omega - \alpha time$

=>time = $\frac {2\omega} {\alpha}$ = 2t

Time to stop = 2t