Question

When 100J of work is done on a fly wheel, it's angular velocity is increased from 60rpm to 180rpm. What is theomens of inertia

Answer 1

Use Work-energy
Change in energy = work done

The energy is rotational
1/2*I*(wf^2 - wi^2) = work

Solve for I
I = 2*work/(wf^2 - wi^2)

Convert from rpm to rad/s
Wi = 60 rpm * (2*pi rad/ 1 rev) *(1 min / 60 s) = 2*pi rad
Wf = 180 rpm = 6*pi rad/s

Plug in numbers
I = 2*100 J / ((6pi rad/s)^2 - (2pi rad/s)^2) = 0.63 kg*m^2