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

Answer:

4.62 s

Explanation:

We are given that

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

$\theta=1\frac{1}{4} rev=\frac{5}{4}\times 2\pi=2.5\pi rad$

$\omega'=0$

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

Substitute the values

$0-(3.4)^2=2\times 2.5\pi \alpha$

$\alpha=\frac{-(3.4)^2}{2\times 2.5\pi}=-0.736 rad/s^2$

$\omega'=\omega+\alpha t$

$0=3.4-0.736 t$

$-0.736t=-3.4$

$t=\frac{-3.4}{-0.736}=4.62 s$

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