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.
