Question

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?

Answer 1

Given, the mass of the solid cylinder is 20 kg, angular velocity is 100  rad/s and radius of cylinder is 0.25 m.

The expression for moment of inertia ( I ) for a solid cylinder of mass m and radius r is,

I= m r 2 2

Substitute the values in above expression.

I= 1 2 ×20× ( 0.25 ) 2 =0.625  kg×m 2

Let the angular velocity be ω, then the rotational kinetic energy K is given as,

K= 1 2 I ω 2

Substitute the values in above expression.

K= 1 2 ×( 0.625 )× ( 100 ) 2 =3125 J

Hence, the rotational kinetic energy of cylinder is 3125 J.

The expression for angular momentum L is,

L=Iω

Substitute the values in above expression,

L=6.25×100 =62.5 J-s

Hence, the value of angular momentum is 62.5 J-s.