A uniform motion of a car along a circular path experiences

Q: What is the answer to NDA (II) 2021 GAT Q118?

B. Correct — B, a change in velocity due to a change in its direction of motion. In uniform circular motion the speed is constant, but velocity is a vector that includes direction, and the direction changes continuously along the circle, so the velocity keeps changing. That changing velocity means the car is accelerating, with a centripetal acceleration directed to the centre, even though its speedometer reading stays fixed. Speed itself does not change, so any option claiming a change in speed is wrong.

(a)a change in speed due to a change in its direction of motion.
(b)a change in velocity due to a change in its direction of motion.
(c)a change in momentum due to no change in its direction of motion.
(d)a constant momentum due to a change in its direction of motion.

Answer

Why

Correct — B, a change in velocity due to a change in its direction of motion. In uniform circular motion the speed is constant, but velocity is a vector that includes direction, and the direction changes continuously along the circle, so the velocity keeps changing. That changing velocity means the car is accelerating, with a centripetal acceleration directed to the centre, even though its speedometer reading stays fixed. Speed itself does not change, so any option claiming a change in speed is wrong.

Why the others are wrong

(a)
a change in speed due to a change in its direction of motion. — The motion is described as uniform, so the speed is constant; only the direction, and hence the velocity, changes.
(c)
a change in momentum due to no change in its direction of motion. — The direction does change all along a circle, so the stated premise is false; momentum changes precisely because the direction changes.
(d)
a constant momentum due to a change in its direction of motion. — Momentum is mass times velocity, a vector, so as the velocity's direction changes the momentum is not constant.

Concept

Uniform circular motion is motion along a circle at constant speed. Because velocity is a vector, the continuous change in direction means the velocity keeps changing even though the speed is fixed, so the body is accelerating and needs a centripetal force directed toward the centre.

The key is that uniform fixes the speed but not the direction. Since velocity and momentum are both vectors, a changing direction changes both even at constant speed, which is why circular motion requires a centripetal force.

Key facts

Speed is a scalar, while velocity is a vector with both magnitude and direction.
In uniform circular motion the speed is constant but the direction, and so the velocity, changes continuously.
A changing velocity means the body is accelerating, with a centripetal acceleration directed to the centre.
Momentum, being mass times velocity, also changes as the direction changes.

An athlete whirling the hammer in a circle inside a throwing cage, illustrating uniform circular motion. — Even though the speed is steady, the direction, and therefore the velocity, changes at every instant, so the motion is accelerated.Image: Pit1233 · Wikimedia Commons (CC0)

Study next

Scalars and vectorsUniform circular motion and centripetal accelerationCentripetal force and everyday examplesDifference between speed and velocityNewton's first law and why a turning body needs a force

Common traps

Equating constant speed with constant velocity.
Thinking no force acts because the speed is steady.

Asked what changes for a body in uniform circular motion; it is the velocity, through its direction, not the speed.

Related PYQs

NDA_GAT_2019_II_Q662019Open & attempt →

A car starts from Bengaluru, goes 50 km in a straight line towards south, immediately turns around and returns to Bengaluru. The time taken for this round trip is 2 hours. The magnitude of the average velocity of the car for this round trip

(a) is 0.
(b) is 50 km/hr.
(c) is 25 km/hr.
(d) cannot be calculated without knowing acceleration.

Answer(a) is 0.

Both turn on velocity being a vector that depends on direction. There the return trip gives zero net displacement and hence zero average velocity; here the constant change in direction keeps changing the velocity even at fixed speed.

Practice

practice — not a real PYQ
A body moves in a circle at constant speed. Which quantity remains constant?
- (a)velocity
- (b)speed
- (c)momentum
- (d)acceleration
Answer(b) speed — velocity, momentum and acceleration keep changing with direction.
practice — not a real PYQ
Uniform circular motion is accelerated motion because
- (a)its speed changes
- (b)its direction, and hence velocity, changes
- (c)no force acts on it
- (d)its mass changes
Answer(b) its direction, and hence velocity, changes.