A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
We need to find Kinetic energy of the rotating cylinder
We know that, Rotational kinetic energy,
KE = 1/2I ω2
Where
I is moment of inertia
ω is angular velocity
Given
Mass of cylinder, M = 20 kg
Radius of cylinder, R = .25 m = 1/4 m
Angular speed of cylinder, ω = 100 rad s-1
Moment of inertia of a solid cylinder, I = 1/2 MR2
I.e. I = 1/2 × 20 × (1/4)2
= 5/8 kg m2
∴ KE = 1/2 I ω2
= 5/16 (100)2
= 3125 J
= 3.125 kJ
We need to find angular momentum of rotating cylinder about its axis.
Angular momentum, L = I ω
We know that,
Moment of inertia of cylinder, I = 5/8 kg m2
Angular speed of cylinder, ω =100 rad s-1
∴ Angular momentum, L = 5/8 × 100
= 62.5 kg m s-1
= 62.5 J s