Question:
A particle is moving in a circular path with constant angular velocity. Its initial angular momentum is L. If the radius of the circle is tripled by keeping angular velocity same, the new angular momentum is:
A particle is moving in a circular path with constant angular velocity. Its initial angular momentum is L. If the radius of the circle is tripled by keeping angular velocity same, the new angular momentum is:
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When angular velocity is constant, the angular momentum is directly proportional to the square of the radius of the circular path.
Updated On: Jun 9, 2026
- \( 3L \)
- \( 6L \)
- \( 9L \)
- \( L/3 \)
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The Correct Option is C
Solution and Explanation
Concept:
Angular momentum \( L \) for a particle of mass \( m \) moving in a circular path is given by the relation \( L = I\omega \), where \( I \) is the moment of inertia and \( \omega \) is the angular velocity. For a point mass, \( I = mr^2 \).
Step 1: Identify the formula for initial angular momentum.
$$ L_{initial} = I_{initial} \times \omega $$ Since \( I_{initial} = mr^2 \): $$ L = mr^2 \omega $$
Step 2: Apply the change in radius.
The radius is tripled, so the new radius \( r' = 3r \). The mass \( m \) and angular velocity \( \omega \) remain unchanged. The new moment of inertia \( I' \) is: $$ I' = m(r')^2 = m(3r)^2 = 9mr^2 = 9I_{initial} $$
Step 3: Calculate the new angular momentum.
$$ L_{new} = I' \times \omega $$ $$ L_{new} = (9I_{initial}) \times \omega $$ $$ L_{new} = 9 \times (I_{initial} \omega) $$ $$ L_{new} = 9L $$ $$\boxed{9L}$$
Step 1: Identify the formula for initial angular momentum.
$$ L_{initial} = I_{initial} \times \omega $$ Since \( I_{initial} = mr^2 \): $$ L = mr^2 \omega $$
Step 2: Apply the change in radius.
The radius is tripled, so the new radius \( r' = 3r \). The mass \( m \) and angular velocity \( \omega \) remain unchanged. The new moment of inertia \( I' \) is: $$ I' = m(r')^2 = m(3r)^2 = 9mr^2 = 9I_{initial} $$
Step 3: Calculate the new angular momentum.
$$ L_{new} = I' \times \omega $$ $$ L_{new} = (9I_{initial}) \times \omega $$ $$ L_{new} = 9 \times (I_{initial} \omega) $$ $$ L_{new} = 9L $$ $$\boxed{9L}$$
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