Angular Momentum in Central Force Field – Rankers Physics
Topic: Rotational Motion
Subtopic: Angular Momentum and Conservation of Angular Momentum

Angular Momentum in Central Force Field

Assertion (A): For a system of particles under central force field, the total angular momentum is conserved.
Reason (R): The torque acting on such a system is zero.
 
(1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
(2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(3) (A) is true but (R) is false
(4) Both (A) and (R) are false

Solution:

Assertion (A) is true, angular momentum is conserved when net torque is zero. Reason (R) is true. For a central force \(\vec{F}\) acting along \(\vec{r}\) (position vector), the torque \(\vec{\tau} = \vec{r} \times \vec{F} = 0\). Since \(\vec{\tau}=0\), \(\frac{\text{d}\vec{\text{L}}}{\text{dt}} = 0\), hence \(\vec{\text{L}}\) is conserved. (R) correctly explains (A).

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