A particle is moving in a circular path with radius r. If the speed of the parti

A particle is moving in a circular path with radius r. If the speed of the particle is doubled, how does its angular momentum change?

A particle is moving in a circular path with radius r. If the speed of the particle is doubled, how does its angular momentum change?

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 of the particle 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. It is given by the formula L = mvr.
Effect of Speed on Angular Momentum – Doubling the speed (v) of the particle while keeping mass (m) and radius (r) constant results in a doubling of angular momentum, since L is directly proportional to v.