Calculating Angular Velocity: Motor at 60rpm Comes to Rest in 10 Revolutions

[pratz]

A motor rotating at 60rpm comes to rest in 10 revolutions with its angular velocity decreasing linearly with angular displacement.Determine it angular velocity as a function of time and determine angular velocity w at t=3 sec..


I need help with this problem...Please someone help...I can't do anything in rotational mechanics:(

 

[cepheid]

Hi Pratz, welcome to PF!

To get you started, you know the that the angular velocity is a linearly decreasing function of angular displacement, meaning that:

$$\omega(\theta) = \omega_0 - C\theta$$​

You know what the inital angular velocity, $\omega_0$ is, because it is given in the problem. You can calculate the constant by noting that the angular velocity equals zero after ten revolutions: $\omega(10 \textfm{rev}) = 0$. Remember to convert everything into radians. Now that you have this function $\omega(\theta)$, you can differentiate it with respect to theta. Can you think of a way of relating that to the time derivative of $\omega$?