Question

A body is moving with constant velocity parallel to x-axis. Its angular momentum w.r.t. the origin will :

• A. be zero
• B. decrease
• C. increase
• D. remain constant

Hint:

If no external force or torque acts, angular momentum is conserved.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Angular momentum of a point mass is \( \vec{L} = \vec{r} \times \vec{p} \). Its magnitude is given by \( L = mvr \sin \phi \), where \( r \sin \phi \) is the perpendicular distance from the origin to the line of motion.
: Key Formula or Approach:
\[ L = m \times v \times r_{\perp} \]
Step 2: Detailed Explanation:
Consider a particle moving with velocity \( \vec{v} \) along a line \( y = h \) (parallel to x-axis).
The position vector \( \vec{r} \) changes as the body moves.
However, the perpendicular distance from the origin to the path of the body is always the vertical distance \( h \).
The magnitude of angular momentum is:
\[ L = m \cdot v \cdot h \]
Since mass \( m \), velocity \( v \), and the perpendicular distance \( h \) are all constant, the angular momentum \( L \) remains constant over time.
Step 3: Final Answer:
The angular momentum remains constant.