📘 Circular Motion: Summary Note

Circular Motion (For MCQ Practice)

Here is a clear and exam-focused Summary Note of the lesson, Circular Motion, specifically tailored for MCQ preparation:

🔹 1. What is Circular Motion?

Circular motion is the motion of an object along a circular path.
The direction of the object continuously changes, so even at constant speed, its velocity changes (because velocity is a vector).

Circular Motion

🔹 2. Types of Circular Motion

Uniform Circular Motion (UCM):
- Speed remains constant
- Velocity continuously changes due to a direction change
- Centripetal force acts towards the centre
Non-uniform Circular Motion:
- Speed changes
- Both the magnitude and direction of velocity change
- Requires centripetal and tangential force

🔹 3. Important Terms & Formulas

Quantity	Symbol	Formula	Unit
Radius of Circle	r	—	metre (m)
Time Period	T	Time for one complete revolution	second (s)
Frequency	f	Revolutions per second = `1/T`	hertz (Hz)
Speed (in UCM)	v	`v = 2πr / T`	m/s
Angular Velocity	ω	`ω = 2π / T = 2πf`	rad/s
Centripetal Acceleration	aᶜ	`a = v² / r` or `ω²r`	m/s²
Centripetal Force	Fᶜ	`F = mv² / r` or `mω²r`	Newton (N)

🔹 4. Centripetal Force

The force that acts towards the centre of the circle
Responsible for changing the direction of velocity
Examples:
- Tension in the string (for a rotating stone)
- Gravitational force (for planets orbiting the sun)
- Friction (for a car on a circular track)

🔹 5. Characteristics of UCM

Speed is constant
Velocity changes due to a direction change
Acceleration is always towards the centre (centripetal)
Centripetal force is essential to keep an object in a circle
No work is done by the centripetal force (force ⊥ displacement)

🧠 MCQ Focus Areas

The distinction between uniform and non-uniform circular motion
Concept of centripetal force and its direction
Formulas for speed, frequency, time period, force, and acceleration
Real-life examples of circular motion
Conceptual questions about the direction of velocity, force, and acceleration

Circular Motion: MCQ Practice Set

🧠 MCQ Quiz Hints

Q1. In uniform circular motion, acceleration is always directed outward from the centre.
✅ Correct Answer:❌ False (It is directed towards the centre.)

Q2. Angular velocity changes with time in uniform circular motion.
✅ Correct Answer:❌ False (Angular velocity is constant.)

Q3. A particle moves in a circle of radius 4 m with a constant speed of 6 m/s. What is the magnitude of its acceleration?

Soln:

a = v²/r = (6²)/4 = 36/4 = 9 m/s²

Hence, the magnitude of its acceleration is 9 m/s².

Q4. A 2 kg mass is attached to a string of length 1.5 m and whirled in a horizontal circle at 4 m/s. What is the tension in the string?

Soln:

T = mv²/r = (2 × 16)/1.5 = 32 / 1.5 = 21.3 N

Hence, tension in the string is 21.3 N.

Q5. An object moves with constant speed in a circular path. What is the work done by the centripetal force in one complete revolution?

✅ Correct Answer: Zero
Reason: Centripetal force is perpendicular to displacement; no work is done.

Q6. A conical pendulum has a length of 1 m and completes one revolution in 2 seconds. What is the angular velocity (ω)?

Soln:

T = 2 s → ω = 2π/T = 2π/2 = π rad/s

Q7. Which of the following forces is not a real force but an effect observed in rotating frames?

✅ Correct Answer: Centrifugal force- As it is a fictitious force observed in a rotating reference frame.

Q8. If mass is doubled and radius is halved for an object in circular motion with the same speed, the centripetal force becomes:

Soln:

Fc = mv²/r → (2m)v²/(r/2) = 4mv²/r → 4 times increase

Note: Here, some terms starting with angular (like angular velocity, angular acceleration, etc) and a few more terms are taken from the NEB syllabus, i.e. out of grade 10(SEE), just for the entrance examination for NEB, Science.