Question

A particle performs uniform circular motion with an angular momentum L. If the frequency of the particle's motion is doubled and its kinetic energy is halved, the angular momentum becomes:

a) L/2
b) L
c) 2L
d) 4L

Answer 1

If the frequency of the particle's motion is doubled and its kinetic energy is halved, the angular momentum becomes 2L.

Step-by-step explanation:

To determine the change in angular momentum, we need to understand the relationship between angular momentum, angular frequency, and kinetic energy. Angular momentum is given by L = Iw, where I is the moment of inertia and w is the angular frequency. If the frequency of the particle's motion is doubled (2w) and its kinetic energy is halved (0.5K), we can use the conservation of angular momentum to find the new angular momentum:

L = Iw = (0.5I)(2w) = 2(Iw) = 2L

The angular momentum becomes 2L, so the correct answer is (c) 2L.