Question

The CORRECT statement for a rigid body rotating about a fixed axis with angular velocity \(\omega\) is

• A. \(\omega\) is directed perpendicular to the axis of rotation
• B. all the particles move with same speed
• C. \(\omega\) is a scalar quantity
• D. \(\omega\) has no direction
• E. different particles move in different circles

Hint:

For a rigid rotator, \(\omega\) is constant for all points, but \(v\) is not constant. The direction of \(\omega\) is given by the right-hand thumb rule.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
For a rigid body rotating about a fixed axis, every particle moves in a circle centered on the axis. The angular velocity is the same for all particles, but linear speed varies with distance from the axis.

Step 2: Detailed Explanation:
Analyze each statement:
• (A) \(\omega\) is directed along the axis of rotation (right-hand rule), not perpendicular to it. Incorrect.
• (B) All particles move with the same angular speed (\(\omega\)), but linear speed (\(v = r\omega\)) is proportional to the distance from the axis. Different particles have different speeds. Incorrect.
• (C) and (D) \(\omega\) is an axial vector; it has both magnitude and direction (along the axis). It is not a scalar. Incorrect.
• (E) Different particles are at different distances from the axis, so they move in different circles (different radii). This is correct.

Step 3: Final Answer:
The correct statement is that different particles move in different circles.