Question

A 150 g baseball is pitched at 42 m/s spinning at 55 rad/s . You can treat the baseball as a uniform solid sphere of radius 4.3 cm .

What fraction of its kinetic energy is rotational?

Answer 1

Mass of the baseball = M = 150 g = 0.15 kg

Radius of the baseball = R = 4.3 cm = 0.043 m

The baseball is considered as a solid uniform sphere.

Moment of inertia of the baseball = I

I = 2MR²/5

I = 2(0.15)(0.043)²/5

I = 1.1094 x 10^-4 kg.m²

Speed of the baseball = V = 42 m/s

Angular speed of the baseball = = 55 rad/s

Total kinetic energy of the baseball = KE

KE = 132.468 J

Rotational kinetic energy of the baseball = KE_R

KE_R = 0.168 J

Ratio of the rotational kinetic energy to the total kinetic energy = F

F = 0.00127

Fraction of the baseball's rotational kinetic energy to the total = 0.00127