Question

If a particle is moving with respect to a chosen origin, it has linear momentum. What conditions must exist for this particle’s angular momentum to be zero about the chosen origin?

a) Particle is stationary.
b) Particle is in linear motion.
c) Particle is in circular motion.
d) Depends on the particle's mass.

Answer 1

A particle's angular momentum can be zero if it is stationary or if its motion is directly towards or away from the origin; hence, either (a) or (b) can be correct conditions for zero angular momentum.

Step-by-step explanation:

Conditions for Zero Angular Momentum

For a particle with linear momentum moving with respect to a chosen origin to have zero angular momentum, it must be moving directly towards or away from the origin, i.e., along the radius vector of the chosen origin. A particle has zero angular momentum about an origin if its velocity vector is parallel (or anti-parallel) to the position vector from the origin to the particle. Therefore, the correct answer is (b) the particle is in linear motion along a line that goes through the origin, or the particle is stationary, answer (a). Circular motion about the origin would produce a nonzero angular momentum, and the particle's mass does not directly determine whether its angular momentum will be zero, making (c) and (d) incorrect.