Determine the rotational momentum of a 10kg diskshaped flywh

Determine the rotational momentum of a 10-kg diskshaped flywheel of radius 9.0 cm rotating with a rotational speed of 320 rad/s. (b) With what magnitude rotational speed must a 10-kg solid sphere of 9.0 cm radius rotate to have the same rotational momentum as the flywheel?

Solution

a)

Moment of Inertia

I=(1/2)MR² =(1/2)*10*0.09²

I=0.0405 Kg-m²

Rotational or angular Momentum is

L=IW =0.0405*320

L=12.96Kg-m²/s

b)

Moment of inertia of solid sphere

I=(2/5)mR² =(2/5)*10*0.09²

I=0.0324 kg-m²

Rotational speed

W=L/I =12.96/0.0324

W=400 rad/sec