Question

A contestants spin a wheel when it is their turn in a game show. One contestant gives the wheel an initial angular speed of 3.40 rad/s. It then rotates through one-and-one-quarter revolutions and comes to rest on the BANKRUPT space. How much time does it take for the wheel to come to rest?

Answer 1

4.62 s

Step-by-step explanation:

We are given that

Initial angular speed,
`\omega=3.4 rad/s`

`\theta=1(1)/(4) rev=(5)/(4)* 2\pi=2.5\pi rad`

`\omega'=0`

`\omega'^2-\omega^2=2\alpha \theta`

Substitute the values

`0-(3.4)^2=2* 2.5\pi \alpha`

`\alpha=(-(3.4)^2)/(2* 2.5\pi)=-0.736 rad/s^2`

`\omega'=\omega+\alpha t`

`0=3.4-0.736 t`

`-0.736t=-3.4`

`t=(-3.4)/(-0.736)=4.62 s`

Hence, the wheel takes 4.62 s to come to rest.