A particle performs uniform circular motion with an angular...

A particle performs uniform circular motion with an angular momentum $L$. If the frequency of particle motion is doubled and its K.E. is halved, the angular momentum becomes:
(a) $2 L$
(b) $4 L$
(c) $\frac{L}{2}$
(d) $\frac{L}{4}$

Key Concepts

Uniform Circular Motion

Uniform circular motion describes the movement of an object along a circular path at a constant speed. Despite the constant speed, the object is accelerating due to the continuous change in direction, and this acceleration is directed towards the center of the circle. This concept is fundamental in understanding how forces and velocities interact in circular trajectories.

Angular Momentum

Angular momentum in the context of circular motion is the measure of the rotational motion of a particle relative to a chosen origin. For a particle moving in a circle, it is calculated as the product of the particle's mass, the square of the radius of the circle, and the angular velocity (or tangential velocity multiplied by the radius). It is a conserved quantity in the absence of external torques.

Kinetic Energy in Circular Motion

The kinetic energy of a particle in circular motion is linked to its speed and is expressed as one half the mass times the square of its velocity. When the velocity is related to the angular speed and the radius of the circle (v = r?), any changes in frequency or angular speed will affect the kinetic energy, illustrating the interdependent nature of these motion parameters.

Frequency and Angular Speed Relationship

Frequency, defined as the number of revolutions per unit time, is directly related to angular speed through the relation ? = 2?f. This connection is crucial in circular motion analysis because changes in frequency directly influence angular velocity, which in turn affects both the kinetic energy and the angular momentum of the particle.

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