Question

Assume that the motor has accelerated the wheel up to an angular velocity ω1 with angular acceleration α in time t1. At this point, the motor is turned off and a brake is applied that decelerates the wheel with a constant angular acceleration of −5α. Find t2, the time it will take the wheel to stop after the brake is applied (that is, the time for the wheel to reach zero angular velocity).

Answer 1

Answer:$t_1\times \frac{1}{5}$

Explanation:

Given

Motor accelerate motor to angular velocity of $\omega _1$

angular acceleration $\alpha$

time taken $t_1$

thus $\omega _1=0+\alpha t_1$

At this point brake is applied that decelerate the wheel with angular acceleration $-5\alpha$

Let us take time taken to be $t_2$

using

$\omega =\omega _0+\alpha t$

where $\omega =final\ angular\ velocity$

$\omega _0=initial\ angular\ velocity$

$\alpha =angular acceleration$

$t=time$

$0=\alpha t_1-5\alpha \cdot t_2$

$t_2=t_1\times \frac{1}{5}$