Question

A sphere of uniform density with mass 15 kg and radius 0.6 m is spinning, making one complete revolution every 0.3 s. The center of mass of the sphere has a speed of 3 m/s. (a) What is the rotational kinetic energy of the sphere

Answer 1

`473.56\ \text{J}`

Step-by-step explanation:

T = Time taken to complete one revolution = 0.3 s

m = Mass of sphere = 15 kg

r = Radius of sphere = 0.6 m

I = Moment of inertia of sphere =
`(2)/(5)mr^2`

Angular speed of the sphere is

`\omega=(2\pi)/(T)=(2\pi)/(0.3)\\\Rightarrow \omega=20.94\ \text{rad/s}`

Rotational kinetic energy is given by

`K_r=(1)/(2)I\omega^2=(1)/(2)* (2)/(5)mr^2\omega^2\\\Rightarrow K_r=(1)/(2)* (2)/(5)* 15* 0.6^2* 20.94^2\\\Rightarrow K_r=473.56\ \text{J}`

The rotational kinetic energy of the sphere is
`473.56\ \text{J}`.