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

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.=(mv^2)/(2)`

`K.E.=(1)/(2)* 0.15* 42^2`

`k.E.=(1)/(2)* 0.15* 1764`

`k.E.=132.3 J`

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

`I=(2)/(5)mr^2=(2)/(5)* 0.15* (0.037)^2`

`I=8.21* 10^(-5) kg-m^2`

Rotational Kinetic Energy

`=(1)/(2)* I* \omega ^2`

`=(1)/(2)* 8.21* 10^(-5)* 45^2`

`=(1)/(2)* 8.21* 10^(-5)* 2025`

`=0.0831 J`