Question

Angular momentum of the particle rotating with a central force is constant due to

• A. constant torque
• B. constant force
• C. constant linear momentum
• D. zero torque

Hint:

Angular momentum remains constant when the torque acting on the system is zero. Central forces do not produce torque as they act along the line connecting the particle to the center of rotation.

Answer 1

The Correct Option is D

Step 1: The angular momentum \( L \) of a particle rotating with respect to a central force is given by: \[ L = r \times p, \] where \( r \) is the position vector, and \( p \) is the linear momentum of the particle. 
Step 2: The rate of change of angular momentum is related to the torque \( \tau \) acting on the particle: \[ \frac{dL}{dt} = \tau. \] 
Step 3: If the torque \( \tau \) is zero, then the angular momentum remains constant. This happens when there is no external torque acting on the particle. 
Step 4: Since central forces always act along the line joining the particle and the center of rotation, they produce zero torque. Therefore, the angular momentum of the particle remains constant.