How long does it take for rotating platform to stop

[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 don't 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?

 

[ehild]

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. ...
I wanted to use the $$\omega= \omega_0+\alpha t$$ equation but i don't know final angular velocity .

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

ehild

 

[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.