Question

A hollow sphere of radius 0.25 m is rotating at 13 rad/s about an axis that passes through its center. the mass of the sphere is 3.8 kg. assuming a constant net torque is applied to the sphere, how much work is required to bring the sphere to a stop?

Answer 1

The work required to bring the sphere to stop is equal to the kinetic energy possessed by the sphere.

Kinetic energy of a rotating body is given by,

K.E = $\frac{1}{2}Iw^{2}$

Here, I= Moment of inertia of hollow sphere,

Since, the hollow sphere is rotating about the axis passing through its center, I =$\frac{2}{3}MR^{2}$

M= Mass of the sphere= 3.8 kg,

R= Radius of gyration= Radius of the sphere= 0.25 m

w= Angular speed of the sphere = 13 rad/s

Substituting the values,

Kinetic energy =$\frac{1}{2} *\frac{2}{3} (3.8)(0.25)^{2}(13.0)^{2}$

= 13.4 J

∴ Work required to bring the sphere to stop is 13.4 J.