Aparticular motor can provide a maximum torque of 110 n • m. assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to 8.13 rad/s?

Using the rotational equivalent of force:

Which is T = I*Alpha

Where: T is torque, I is the moment of inertia and Alpha is the angular acceleration. 

This is for the flywheel: J = 1/2mr^2 = 5*3^2 = 45 kgm^2 

From the equation: 

T = J*dω/dt 

we get: 

Δt = J*Δω/T = 45*8.13/110.0 = 3.326 sec

pe = weightxheight = 2000x1000=2,000,000joules