Question

A bowling ball has a mass of 3.7kg, a moment of inertia of 0.340992kg*m^2, and a radius of 0.48m. It rolls along the lane without slipping at a linear speed of 3.2m/s. What is the total kinetic energy of the rolling ball. Answer in units of J.

Answer 1

Kinetic energy due to linear motion:


`E= (1)/(2)mv^2= (1)/(2)3.7(3.2)^2=18.944J`

The angular velocity is found by


`v=r \omega`


`\omega = (v)/(r)= (3.2)/(0.48) =6.667rad/s`

Kinetic energy due to rotational motion:


`E= (1)/(2)I \omega^2 = (1)/(2)0.340992(6.667)^2=7.5776J`
Then

`E_(total)=18.944J+ 7.5776J=26.5216J`