## Explanation

Angular momentum(L) : It is an measure of the rotation of body, taking into account its mass , shape and speed.

L = r × p

where r is distance from the axis of rotation and the p is the linear momentum of the body.

Torque (τ) : It is an moment of force i.e. tendency of a force to rotate an object about an axis.

τ = r × f

where r is the perpendicular distance from the axis of the rotation and f is the applied force.

As we know ,

L = r × p

differentiating both sides with respect to t

dL/dt = r × (d p / dt) + p × (d r / dt)

dL/dt = r × f + m(v × v)

dL/dt = τ + 0

τ = dL/dt

**Hence , the relationship between torque and angular momentum.**