Question

The angular momentum of a moving body remains constant, if

• A. net external force is applied
• B. net pressure is applied
• C. net external torque is applied
• D. net external torque is not applied

Hint:

Compare with linear momentum: Linear momentum is conserved if no net external \textbf{force} acts. Angular momentum is conserved if no net external \textbf{torque} acts. Both are direct consequences of Newton's laws.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks for the condition under which the angular momentum of a system remains conserved.
Step 3: Detailed Explanation:
The principle of conservation of angular momentum states that the total angular momentum of a system remains constant if no external torque acts on it.
Mathematically, the relationship between torque (\( \vec{\tau} \)) and angular momentum (\( \vec{L} \)) is given by:
\[ \vec{\tau} = \frac{d\vec{L}}{dt} \]
If the net external torque (\( \vec{\tau} \)) acting on the body is zero, then \( \frac{d\vec{L}}{dt} = 0 \), which implies that the angular momentum \( \vec{L} \) is constant.
- Option (1) refers to force, which causes a change in linear momentum, not necessarily angular momentum (unless the force also produces a torque).
- Option (2) refers to pressure, which is force per unit area and not directly related to angular momentum conservation in this context.
- Option (3) suggests that if net external torque is applied, angular momentum is constant, which is the opposite of the principle.
Step 4: Final Answer:
The angular momentum of a moving body remains constant if no net external torque is applied.