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.