Define radius of gyration. Write its physical significance.

Radius of gyration is defined as the distance axis of rotation to a point where the total mass of the body is supposed to concentrate. Moment of inertia I = m k 2 Where, M = mass of body k= Radius of Gyration SI unit of Radius of gyration is metre. Physical significance: 1. If the particles of the body are distributed close to the axis of rotation, the radius of gyration is less. 2. If the particles are distributed away from the axis of rotation, the radius of gyration is more.

State and prove principle of conservation of angular momentum.

Principle of conservation of angular momentum: It states that if no external torque acts on a system, the total angular momentum of the system remains constant. We know that L → = r → × p → Differentiating both sides w.r.t time t, we get d L → d t = d d t r → × p → = d r → d t × p → + r → × d p → d t Now d r → d t = v → , d p → d t = F → , p → = m v → Hence d L → d t = v → × m v → + r → × F → Now v → × v → = 0 → , r → × F → = τ → Hence d L → d t = τ → Hence if τ → = 0 , d L → d t = 0 ⇒ L → = constant Hence proved.