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A particle moves in a circular path with a radius r and a constant speed v. If t

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Question: A particle moves in a circular path with a radius r and a constant speed v. If the speed is doubled, what happens to the angular momentum of the particle?

Options:

  1. It remains the same
  2. It doubles
  3. It quadruples
  4. It halves

Correct Answer: It doubles

Solution: 

Angular momentum L = mvr; if v is doubled, L also doubles.

A particle moves in a circular path with a radius r and a constant speed v. If t

Practice Questions

Q1
A particle moves in a circular path with a radius r and a constant speed v. If the speed is doubled, what happens to the angular momentum of the particle?
  1. It remains the same
  2. It doubles
  3. It quadruples
  4. It halves

Questions & Step-by-Step Solutions

A particle moves in a circular path with a radius r and a constant speed v. If the speed is doubled, what happens to the angular momentum of the particle?
  • Step 1: Understand that angular momentum (L) is calculated using the formula L = mvr, where m is mass, v is speed, and r is the radius of the circular path.
  • Step 2: Identify that if the speed (v) of the particle is doubled, we can represent the new speed as 2v.
  • Step 3: Substitute the new speed into the angular momentum formula: L' = m(2v)r.
  • Step 4: Simplify the new angular momentum: L' = 2(mvr).
  • Step 5: Notice that mvr is the original angular momentum (L), so L' = 2L.
  • Step 6: Conclude that if the speed is doubled, the angular momentum also doubles.
  • Angular Momentum – Angular momentum (L) is the product of the mass (m), velocity (v), and radius (r) of the circular path, expressed as L = mvr.
  • Effect of Speed on Angular Momentum – Doubling the speed (v) of a particle in circular motion results in a direct doubling of its angular momentum, since L is directly proportional to v.
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