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* (1)/(5)`

Step-by-step 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* (1)/(5)`