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?
It remains the same
It doubles
It quadruples
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.
