Question

Which of the following is true in uniform circular motion?
\[{\text{A}}{\text{.}}\] Both the angular velocity and the angular momentum vary
\[{\text{B}}{\text{.}}\] The velocity varies but the momentum remains constant
\[{\text{C}}{\text{.}}\] Magnitude of both the velocity and the momentum stay constant
\[{\text{D}}{\text{.}}\] The momentum varies but the velocity remains constant

Answer 1

Hint: Here, we will proceed by defining the terms linear velocity and angular velocity. Then, we will also discuss the uniform circular motion. Finally, we will be talking about the acceleration in a uniform circular motion.

Complete step-by-step solution:

Linear velocity in uniform circular motion has the path along the tangent to the circle created by the body in a uniform circular motion, which is always changing. But the magnitude is constant in linear velocity. Angular velocity has a direction perpendicular to the plane of uniform circular motion provided by the right-hand rule and its magnitude is constant since it always covers equal angular displacement.
Uniform circular motion can be defined as the motion of an object moving at a constant speed in a circle. As an object moves around in a circle, its trajectory is continuously changing. The object is moving tangentially to the circle at all times. Since the direction of the velocity vector is identical to that of the motion of the body, the velocity vector is also oriented tangentially to the circle.
An object which moves in a circle accelerates. Accelerating objects are objects which change their velocity either the velocity vector magnitude (i.e., speed) or the direction of motion. The object which is moving in ‘a’ uniform circular motion is accelerating because of the change in the direction of the velocity.
Since velocity is a vector quantity and depends upon the direction of motion. Momentum is also a vector quantity because it depends on the velocity which is in itself a vector quantity. Since velocity is not constant so the momentum will also not remain constant. This is due to the change in direction of motion. But the magnitudes of velocity (i.e., speed), the magnitude of momentum is constant
Speed, kinetic energy, the magnitude of linear momentum magnitude, the momentum of angular momentum is also constant in a uniform circular motion.
Therefore, the magnitude of both the velocity and momentum remains constant.

Hence, option C is correct.

Note: Speed is the amount of the distance covered in a unit time by a body and is constant in a uniform circular motion. Angular velocity is basically defined as the rate of change of angular displacement. An object undergoing uniform circular motion travels at a constant speed.