Physics · System Of Particles And Rotational Motion · NEET
Yes. For a single particle, angular momentum is L = r x p. Differentiating with respect to time: dL/dt = (dr/dt x p) + (r x dp/dt). The first term is v x mv = 0 (a vector crossed with itself is zero). The second term is r x F, which is the torque tau. So dL/dt = tau. This is the exact rotational analogue of Newton's second law F = dp/dt.
They are the same law written differently. tau = dL/dt is the general form and always works. For a rigid body rotating about a fixed axis with a constant moment of inertia I, L = I omega, so dL/dt = I (d omega/dt) = I alpha. So tau = I alpha is just the special case when I stays constant. If I changes (like a spinning skater pulling arms in), you must use tau = dL/dt.
If the total external torque is zero, then dL/dt = 0, which means L does not change with time. So L stays constant. This is the conservation of angular momentum. A spinning ice skater, a planet orbiting the Sun, and a diver curling up all keep L fixed because no net external torque acts on them.
Only the external torque matters. Inside a system, internal forces between particles come in action-reaction pairs along the line joining them, so their torques cancel out in total. NCERT states: the time rate of the total angular momentum of a system about a point equals the sum of the external torques about the same point. So dL/dt = tau_external.
Yes, always. Both tau and L must be measured about the same origin (reference point). If you shift the origin, both quantities change, but the relation tau = dL/dt still holds as long as you use the same point for both. Mixing points gives wrong answers in NEET problems.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Torque equals the rate of change of angular momentum: tau = dL/dt. This means torque is what changes the angular momentum of a body over time, exactly as force changes linear momentum (F = dp/dt).
Yes, but only the external torque counts. The time rate of change of the total angular momentum of a system equals the sum of the external torques acting on it, because internal torques cancel in action-reaction pairs.
When the net external torque is zero, dL/dt = 0, so angular momentum L stays constant. This is the law of conservation of angular momentum, used for spinning skaters, planets, and rotating stools.
Start with L = r x p. Differentiate: dL/dt = (v x mv) + (r x F). The first term is zero because v is parallel to mv. The second term r x F is the torque tau. Hence dL/dt = tau.
It is the master equation for rotational dynamics. From it you get tau = I alpha (constant I) and conservation of angular momentum (zero torque). NEET tests both special cases, so understanding the parent relation lets you solve any rotation problem.
