How long does it take for rotating platform to stop

1. Nov 24, 2004

Alem2000

Hi my problem is I have a platform that is rotating and it $$\omega_0=8\pi$$ and the question is how long does it take it to stop. All my work up to here is correct and I have $$\sum\tau=I\alpha$$ where my $$\sum\tau=3.75Nm$$ and $$I=1.91kgm^2$$ and $$\alpha=1.96rad/s^2$$ so I wanted to use the $$\omega= \omega_0+\alpha t$$ equation but i dont know final angular velocity and time is my target variable. The solution manual used $$\omega=\alpha t$$ why is this justified? The $$\omega_0$$ does not equal zero so why did the solution manual just take it out?

2. Nov 24, 2004

ehild

The final state is when the platform stops, it means does not rotate, is not the final angular velocity zero then??? :rofl:

ehild

3. Nov 24, 2004

krab

The final $\omega$ is zero. So you have
$$0=\omega_0+\alpha t$$
$\alpha$ is actually negative (angular speed decreasing), and you know the initial angular speed, so solve the above equation for t and you're done.