Question

A baseball has a mass of 0.15 kg and radius 3.7 cm. In a baseball game, a pitcher throws the ball with a substantial spin so that it moves with an angular speed of 45 rad/s and a linear speed of 42 m/s. Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball in joules.

Answer 1

Answer:

Explanation:

Given

mass of baseball $m=0.15 kg$

radius of ball $r=3.7 cm$

angular speed of ball $\omega =45 rad/s$

linear speed of ball $v=42 m/s$

Transnational Kinetic Energy is given by

$K.E.=\frac{mv^2}{2}$

$K.E.=\frac{1}{2}\times 0.15\times 42^2$

$k.E.=\frac{1}{2}\times 0.15\times 1764$

$k.E.=132.3 J$

Considering the ball as solid sphere its moment of inertia is given by  

$I=\frac{2}{5}mr^2=\frac{2}{5}\times 0.15\times (0.037)^2$

$I=8.21\times 10^{-5} kg-m^2$

Rotational Kinetic Energy

$=\frac{1}{2}\times I\times \omega ^2$

$=\frac{1}{2}\times 8.21\times 10^{-5}\times 45^2$

$=\frac{1}{2}\times 8.21\times 10^{-5}\times 2025$

$=0.0831 J$