A rotating uniform cylindrical platform of mass 235 kg and r

A rotating uniform cylindrical platform of mass 235 kg and radius 5.5 m slows down from 3.8 rev/s to rest in 16 s when the driving motor is disconnected.

Estimate the power output of the motor (hp) required to maintain a steady speed of 3.8 rev/s.

Express your answer using three significant figures.

Solution

Moment of Inertia

I=(1/2)MR² =(1/2)*235*5.5²=3554.4 Kg/m²

1 rev =2pi rad

angular acceleration

alpha =W/t =(3.8*2pi)/16

alpha =1.4922 rad/s²

Torque

T=I*alpha =3554.4*1.4922

T=5304 N-m

Power output of the motor is

P=TW =5304*(3.8*2pi)

P=126640 Watss

1 HP =745.7 W

P=126640/745.7

P=169.83 hp =170 hp (approx)