Question

A bowling ball has a mass of 1.3 kg, a moment of inertia of 0.075088 kg · m2 , and a radius of 0.38 m. It rolls along the lane without slipping at a linear speed of 3 m/s. What is the total kinetic energy of the rolling ball? Answer in units of J.

Answer 1

Answer:

8.19 Joules

Explanation:

m = Mass of ball = 1.3 kg

I = Moment of inertia = 0.075088 kgm²

r = Radius of ball = 0.38 m

v = Linear speed = 3 m/s

Angular speed

$\omega=\frac{v}{r}$

The linear and rotational kinetic energy will give us the total kinetic energy

$K=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2\\\Rightarrow K=\frac{1}{2}(mv^2+I\omega^2)\\\Rightarrow K=\frac{1}{2}\left(mv^2+I\left(\frac{v}{r}\right)^2\right)\\\Rightarrow K=\frac{1}{2}\left(1.3\times 3^2+0.075088\times \left(\frac{3}{0.38}\right)^2\right)\\\Rightarrow K=8.19\ J$

The  total kinetic energy of the rolling ball is 8.19 Joules