A massless rod S having length 2l has equal point masses attached to its two ends as shown in figure. The rod is rotating about an axis passing through its centre and making angle α with the axis. The magnitude of change of momentum of rod i.e. ||dL/dt|| equals

We know, that rate of change of angular momentum is equal to the torque acting on the system.
→ ||dL/dt|| = τ
From the figure, Force on the mass m is given as:
F = mrω² (Due to centripetal force)
r = lSinα
F = m × lSinα × ω²
→ τ = rperpendicular × F
rperpendicular = lCosα
→ τ = l Cosα × m lSinα ω²
τ = ml²ω²SinαCosα
Since α = θ, therefore
τ = ml²ω²SinθCosθ
2τ = 2ml²ω²SinθCosθ = ml²ω²(2SinθCosθ) = ml²ω²Sin2θ
Therefore, ||dL/dt|| = ml²ω²Sin2θ