Question

Name a physical quantity that remains constant in a uniform circular motion
(A) Velocity
(B) Acceleration
(C) Momentum
(D) Angular speed

Answer 1

Hint As we know that in a uniform circular motion the speed remains constant but velocity and acceleration are a vector quantity, so it will keep changing with the change in the direction. The speed is a scalar quantity so it is independent of direction.

Complete step by step answer
It is given in the question to name a physical quantity that remains constant in a uniform circular motion.
We know that the object moving in a circular path is said to be in a circular motion and if the object is moving in a circular path with constant speed then it is said to be in a uniform circular motion.
The speed is a scalar quantity and it is independent of direction whereas velocity is a vector quantity therefore, the velocity of the object keeps on change because of the change in its direction.
We also know that acceleration is defined as the change in velocity per unit time it means acceleration is also a vector quantity and it will also change if the direction changes.
Momentum is equal to the product of the mass of the object and its velocity, it means the momentum is directly proportional to the velocity. If the velocity changes then the momentum will also change accordingly.
 \[p = mv\]
 \[p \propto v\]
Here, ‘p’ is the momentum of the object, ‘m’ is the mass of the object and ‘v’ is the velocity of the object.
So, the velocity, acceleration, and momentum of the body are vector quantities, so they will keep on changing with the change in the direction of the object. But the speed is a scalar quantity and it is independent of direction therefore, the speed is the only physical quantity that remains constant among the given options.

Thus, option D is correct.

Additional information
Please keep in mind that during uniform circular motion the magnitude of velocity and acceleration remains constant but as these physical quantities are vector quantities, they change with the change in direction without changing its magnitude.

Note
One can easily confuse the word ‘angular’ and they may think that angular speed is different from speed; as a result, they may tick the wrong option as their answer. But it is noted that angular speed and speed both are representing the same physical quantity. We generally add the word ‘angular’ before speed to clear that this speed is representing the speed of an object in a circular path.