Question

Determine the kinetic energy of a circular disc rotating with a speed of 60 r.p.m. about an axis passing through a point on its circumference and perpendicular to its plane. the circular disc has a mass of 5 kg and radius 1 m.

Answer 1

given, mass of circular disc , m = 5 kg

radius of circular disc , r = 1m

and angular speed , w = 60 r.p.m = 60 × 2π/60 = 2π rad/s

we know, rotational kinetic energy , K = 1/2 Iw² , where I is moment of inertia about axis of rotation.

so first of all, we should find out moment of inertia about axis of rotation.

a/c to question,

disc rotating about an axis passing through a point on its circumference and perpendicular to its plane.

step 1 : moment of inertia about centre of mass of disc , Icm = 1/2 mr²

step 2 : moment of inertia about an axis passing through circumference and perpendicular to its plane, I = Icm + mr²

= 1/2 mr² + mr²

= 3/2 mr²

= 3/2 × 5 × (1)²

= 7.5 kgm²

now, kinetic energy = 1/2 × 7.5 × (2π)² J

= 1/2 × 7.5 × 4π²

= 15π² J