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 50 rad/s and a linear speed of 48 m/s. Assuming the baseball to be a uniform solid sphere, determine the rotational and translational kinetic energies of the ball.

Answer 1

Rotational kinetic energy is 0.513 j

Transnational kinetic energy is 172.8 j

Step-by-step explanation:

We have given mass of the baseball m = 0.15 kg

radius r = 3.7 cm = 0.037 m

Angular velocity is given as
`\omega =50rad/sec`

Linear velocity v = 48 m/sec

We know that moment of inertia is given by
`I=(1)/(2)mr^2=(1)/(2)* 0.15* 0.037^2=1.026* 10^(-4)kgm^2`

Now rotational kinetic energy is given by

`KE_(rotational)=(1)/(2)* 1.026* 10^(-4)* 50^2=0.513j`

Now transnational kinetic energy is given by
`KE_(translational)=(1)/(2)mv^2=(1)/(2)* 0.15* 48^2=172.8j`