A particle is moving along a straight line parallel to x...

A particle is moving along a straight line parallel to $x$ -axis with constant velocity. Its angular momentum about the origin
(a) decreases with time.
(b) increases with time.
(c) remains constant.
(d) is zero.

Key Concepts

Conservation of Angular Momentum

Conservation of angular momentum is a fundamental principle in mechanics stating that if no external torque acts on a system, its total angular momentum remains constant over time. This concept is critical in analyzing systems where constant velocity or absence of external rotational forces implies that the angular momentum does not change.

Torque

Torque is the measure of the force that can cause an object to rotate about an axis, defined as the cross product of the position vector and the force vector. It represents the rate of change of angular momentum, so when the net external torque on a system is zero, the angular momentum remains unchanged.

Angular Momentum

Angular momentum is a measure of the rotational motion of an object about a point, defined for a particle as the cross product of its position vector and its linear momentum. It encapsulates both the magnitude of the momentum and how far the particle is from the point of reference, playing a central role in the study of rotational dynamics.

Vector Cross Product

The vector cross product is a mathematical operation on two vectors that produces a third vector, which is perpendicular to the plane containing the original vectors. In the context of angular momentum, the cross product of the position vector and the momentum vector determines both the magnitude and direction of the angular momentum.

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