#### 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 the angular momentum of the cylinder about its axis?

#### Solution 1

Mass of the cylinder, *m* = 20 kg

Angular speed, *ω* = 100 rad s^{–1}

Radius of the cylinder, *r* = 0.25 m

The moment of inertia of the solid cylinder:

`I = (mr^2)/2`

`= 1/2 xx 20 xx (0.25)^2`

= 0.625 `"kg m"^2`

:.Kinetic energy = `1/2Iomega^2`

`= 1/2 xx 6.25 xx (100)^2 = 3125J`

∴Angular momentum, L = Iω

= 6.25 × 100

= 62.5 Js

#### Solution 2

M = 20 kg

Angular speed, w = 100 rad s^{-1}; R = 0.25 m

Moment of inertia of the cylinder about its axis =1/2 MR^{2} = 1/2 x 20 (0.25)^{2} kg m^{2} = 0.625 kg m^{2}

Rotational kinetic energy,

E_{r} = 1/2 Iw2 = 1/2 x 0.625 x (100)^{2} J = 3125 J

Angular momentum, L = I_{w} = 0.625 x 100 J_{s}= 62.5 J_{s}