A sphere of mass m and radius r is attached to the rim of a disk (mass M, radius

Question

A sphere of mass m and radius r is attached to the rim of a disk (mass M, radius R). The disk is rotating counter-clockwise with a constant period T around an axis through the center of the disk. Neglect friction. If the disk has a radius R=0.4 m and a mass M=0.6 kg, and the sphere has a radius r=0.02 m and a mass m=0.32 kg, and if the period of rotation is T=6 s, what is the magnitude of the velocity of the sphere? What is the magnitude of the angular velocity of the disk? What is the moment of inertia of the whole contraption around the axis through the center of the disk?

Explanation / Answer

V = 2*pi*R/T = (0.4*2*3.14)/6 =0 .4186 m/s

w = 2pi/T = 1.05 rad/s

I = 0.5M*R^2 + mR^2

I = (0.5*0.6*0.4*0.4)+(0.32*0.4*0.4) = 0.0992 kg m^2

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