medium difficulty7 min

Uniform Circular Motion

Uniform circular motion is motion along a circular path with constant speed, while the direction of velocity changes continuously.

In one line: Same speed, new direction, changing velocity.

Practice This Concept

Understand it

In circular motion, the object covers equal distances in equal intervals of time if speed is constant. Still, velocity changes because its direction is different at different points of the circle. This means the object is accelerating even at constant speed.

Example

A stone tied to a string and whirled at steady speed is in uniform circular motion.

Rule to remember

For one complete round, speed = circumference / time = 2πr / T, where r is radius and T is time period.

Velocity direction is tangent to the circle at each point.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A toy car moves around a circular track of radius 7 m in 11 s.

1Distance in one round = 2πr = 44 m approximately.
2Speed = 44/11 = 4 m/s, but its velocity changes at every point because direction changes.

Method you can reuse

1Check if path is circular.
2Check if speed is constant.
3State that direction changes at every point.
4If asked for speed in one round, use 2πr divided by time period.

Sketch it in your answer

Draw a circle with velocity arrows tangential at different points and an inward direction change shown toward the centre.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why is uniform circular motion called accelerated motion?

Think first, then show answer

Uniform circular motion is called accelerated motion because velocity changes continuously due to change in direction, even though speed remains constant.

Common wrong answer

Saying acceleration is zero because speed is constant.

Why it loses marks: Velocity also depends on direction.

Don't mix this up

Students often think constant speed means zero acceleration in all cases, but direction change also changes velocity.

Exam tip

For circular motion, mention both points: speed is constant, but velocity changes because direction changes.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Questions may ask why constant-speed circular motion is accelerated or ask for speed using 2πr/T.

1
Enough for 1 mark
Uniform circular motion is motion along a circular path with constant speed, while the direction of velocity changes continuously.
2
Add for 2 marks
Example: A stone tied to a string and whirled at steady speed is in uniform circular motion.
3
Add for 3 marks
In circular motion, the object covers equal distances in equal intervals of time if speed is constant.

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