Question

The center of mass of a pitched baseball or radius 1.65 cm moves at 28.2 m/s. The ball spins about an axis through its center of mass with an angular speed of 69.1 rad/s. Calculate the ratio of the rotational energy to the translational kinetic energy. Treat the ball as a uniform sphere. 

Answer 1

The translational kinetic energy is

$$E_T=\frac12 mv^2.$$

The rotational kinetic energy is

$$E_R=\frac12 I\omega^2=\frac12\cdot\frac25mr^2\omega^2=\frac15mr^2\omega^2.$$

The ratio is

$$k=\frac{E_R}{E_T}=\frac{2r^2\omega^2}{5v^2}=6.5\cdot10^{-4}.$$