Question

A mass '$M$' is moving with constant velocity parallel to X-axis. Its angular momentum with respect to the origin is

• A. constant
• B. zero
• C. decreasing
• D. increasing

Hint:

Angular momentum is constant whenever a particle moves at a constant velocity because the impact parameter (perpendicular distance) to any fixed origin stays constant.

Answer 1

The Correct Option is C

Step 1: Angular momentum $\vec{L}$ of a particle relative to a point is defined as $\vec{L} = \vec{r} \times \vec{p}$, where $\vec{p} = M\vec{v}$.
Step 2: The magnitude of angular momentum can be expressed as $L = Mvh$, where $h$ is the perpendicular distance from the reference point (origin) to the line of motion of the particle.
Step 3: The mass moves with a constant velocity parallel to the X-axis. This means its speed $v$ is constant and its y-coordinate (which is the perpendicular distance $h$ from the origin) remains constant over time.
Step 4: Since $M$, $v$, and $h$ are all constant, the magnitude $L = Mvh$ is constant. The direction of $\vec{L}$ also remains unchanged as the motion is in a straight line.