A particle performing uniform circular motion has angular...

A particle performing uniform circular motion has angular momentum $L$., its angular frequency is doubled and its $K . E$. halved, then the new angular momentum is
$\{\mathrm{A}\} 1 / 2$
\{B $\} 1 / 4$
$\{\mathrm{C}\} 2 \mathrm{~L}$
$\{\mathrm{D}\} 4 \mathrm{~L}$

Key Concepts

Angular Momentum

Angular momentum is a measure of the rotational motion of an object and is defined as the product of the moment of inertia and the angular velocity. It is a key quantity conserved in isolated systems with no external torques, and it helps describe the rotational state of a system.

Uniform Circular Motion

Uniform circular motion describes the motion of an object moving at a constant speed along a circular path. Despite the constant speed, there is centripetal acceleration directed towards the center of the circle, which maintains the circular path.

Angular Frequency

Angular frequency, denoted by ?, represents the rate at which an object rotates or revolves, measured in radians per second. It directly influences both angular momentum and the rotational kinetic energy of a system, as changes in ? typically affect these quantities.

Rotational Kinetic Energy

Rotational kinetic energy is the energy due to an object’s rotational motion and is given by the expression 1/2 I ?², where I is the moment of inertia. This concept links the rotational speed of an object with the energy stored in its motion.

Moment of Inertia

The moment of inertia quantifies how much resistance an object offers to changes in its rotational state about a given axis. It plays a critical role in determining both the angular momentum and the rotational kinetic energy, acting as a rotational analogue to mass in linear motion.

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