Question

A uniform, 8.40-kg, spherical shell 52.0 cm in diameter has four small masses of mass 2.20-kg attached to its outer surface and equally spaced around it. This combination is spinning about an axis running through the center of the sphere and two of the small masses

What friction torque is needed to reduce its angular speed from 80.0 rpm to 45.0 rpm in a time interval of 33.0 s ?

Answer 1

Frictional Torque = (moment of inertia)*(angular deceleration)

Angular deceleration = [(80 rpm - 45 rpm)(2 pi radians/rev)(1 min/60 s)] / 33 s = 0.111 rad/s^2

Moment of inertia = [(2/3)(8.4 kg)(0.52 m / 2)^2 for the spherical shell] + 2[0 for the two small masses going through the axis of rotation] + 2[(2.2 kg)(0.52 m / 2)^2] for the two masses a sphere radius distance from the axis of rotation] = 0.676 kg m^2

Frictional torque needed = (0.676 kg m^2)(0.111 rad/s^2) = 0.075 N.m