Uniform Circular Motion Notes for NEET Physics Students

Uniform Circular Motion Explained Easily for Beginners

 - Dr.Sanjaykumar pawar

UNIFORM CIRCULAR MOTION (UCM)

│

├── Definition

│   ├── Motion in circular path

│   ├── Speed remains constant

│   └── Direction changes continuously

│

├── Important Features

│   ├── Circular path

│   ├── Constant speed

│   ├── Changing velocity

│   └── Acceleration present

│

├── Velocity in UCM

│   ├── Acts along tangent

│   ├── Tangent to circle

│   └── Perpendicular to radius

│

├── Acceleration in UCM

│   ├── Due to change in direction

│   ├── Called centripetal acceleration

│   ├── Always towards centre

│   └── Perpendicular to velocity

│

├── Centripetal Acceleration

│   │

│   ├── Formula

│   │   └── ac = v² / R

│   │

│   ├── Depends on

│   │   ├── Speed (v)

│   │   └── Radius (R)

│   │

│   └── Direction

│       └── Towards centre

│

├── Angular Velocity Relation

│   ├── v = ωR

│   └── ac = ω²R

│

├── Change in Velocity (Δv)

│   ├── Velocity changes at every point

│   ├── Δv points towards centre

│   └── Causes acceleration

│

├── Examples

│   ├── Rotating fan

│   ├── Earth around Sun

│   ├── Stone tied to string

│   └── Car on circular road

│

├── NEET Important Points

│   ├── Speed constant

│   ├── Velocity not constant

│   ├── Accelerated motion

│   ├── Velocity tangent to path

│   └── Acceleration centre-seeking

│

├── Frequently Asked Concepts

│   ├── Why acceleration exists?

│   │   └── Due to changing direction

│   │

│   ├── Is velocity constant?

│   │   └── No

│   │

│   ├── Is speed constant?

│   │   └── Yes

│   │

│   └── Direction of acceleration?

│       └── Towards centre

│

└── Memory Trick

    ├── Velocity → Tangent

    └── Acceleration → Centre

Diagram showing velocity and centripetal acceleration in uniform circular motion.

Internal Links

Motion in a Plane Notes

Projectile Motion Complete Notes

Laws of Motion NEET Notes

Vectors Physics Notes

Circular Motion Formula Sheet

Kinematics Class 11 Notes

Newton’s Laws of Motion Explained

Relative Velocity Notes

Work, Energy and Power Notes

Rotational Motion Basics

Uniform Circular Motion (UCM)

Definition of Uniform Circular Motion

When an object moves along a circular path with constant speed, the motion is called Uniform Circular Motion (UCM).

Important Points:

• Path of motion is circular
• Speed remains constant
• Direction of velocity changes continuously
• Hence acceleration is present

Examples of Uniform Circular Motion

• A stone tied to a string and rotated
• Earth revolving around the Sun
• Fan blades rotating
• A car moving on a circular track

Why Acceleration Exists in UCM?

Although the speed is constant, velocity changes because direction changes continuously.

Velocity depends on:

• Magnitude (speed)
• Direction

Therefore, changing direction means changing velocity. Hence acceleration exists.

Velocity in Circular Motion

At every point on the circular path, velocity acts along the tangent to the circle.

Key Point: Velocity is always perpendicular to the radius vector.

Change in Velocity (Δv)

Suppose:

• Velocity at point P = v
• Velocity at point P′ = v′

Since directions are different, there is a change in velocity.

Δv = v′ − v

This change in velocity points towards the centre of the circle.

Direction of Acceleration

Average acceleration acts in the direction of Δv.

Hence acceleration is directed towards the centre of the circle.

Conclusion: Acceleration in uniform circular motion always acts towards the centre. This acceleration is called Centripetal Acceleration.

Centripetal Acceleration

The word:

• Centri → centre
• Petal → seeking

So centripetal acceleration means centre-seeking acceleration.

Derivation of Centripetal Acceleration

a_c = v² / R

Where:

• a_c = centripetal acceleration
• v = speed of object
• R = radius of circular path

Step 1: Formula of acceleration

a = Δv / Δt

Step 2: Similar triangle relation

Δv / v = Δr / R

Therefore,

Δv = vΔr / R

Step 3: Substitute in acceleration formula

a = Δv / Δt

Substituting value of Δv:

a = vΔr / RΔt

Step 4: For very small time interval

When Δt becomes very small:

Δr ≈ vΔt

Substituting:

a = v(vΔt) / RΔt

a = v² / R

Final Formula

a_c = v² / R

Direction of Centripetal Acceleration

• Always towards the centre
• Perpendicular to velocity
• Changes direction of velocity only

Important Characteristics of UCM

Quantity	Nature
Speed	Constant
Velocity	Changes continuously
Acceleration	Present
Direction of acceleration	Towards centre
Type of acceleration	Centripetal acceleration

Important NEET Formulae

Velocity relation

v = ωR

Where:

• ω = angular velocity

Centripetal acceleration using angular velocity

a_c = ω²R

Important NEET Concepts

• Uniform circular motion is accelerated motion
• Speed remains constant
• Velocity changes continuously
• Centripetal acceleration acts towards centre

Frequently Asked Questions

Q1. Is uniform circular motion accelerated motion?

Yes. Velocity changes continuously due to changing direction.

Q2. Is velocity constant in UCM?

No. Only speed remains constant.

Q3. Why is acceleration called centripetal acceleration?

Because it always acts towards the centre of the circle.

Q4. What changes due to centripetal acceleration?

Only direction of velocity changes.

Quick Revision

• Circular path + constant speed = Uniform Circular Motion
• Velocity changes due to changing direction
• Acceleration acts towards centre
• Centripetal acceleration formula = v²/R
• Velocity is tangent to the circle

Memory Trick

Velocity → Tangent
Acceleration → Centre

Uniform Circular Motion Questions and Answers

Multiple Choice Questions (MCQs)

1. In uniform circular motion, the speed of the object is:

A. Variable
B. Zero
C. Constant
D. Infinite

Answer: C. Constant

2. In uniform circular motion, acceleration is directed:

A. Away from centre
B. Along tangent
C. Towards centre
D. Upward

Answer: C. Towards centre

3. The acceleration in circular motion is called:

A. Tangential acceleration
B. Linear acceleration
C. Centripetal acceleration
D. Gravitational acceleration

Answer: C. Centripetal acceleration

4. The SI unit of centripetal acceleration is:

A. m
B. m/s
C. m/s²
D. N

Answer: C. m/s²

5. The formula of centripetal acceleration is:

A. vR
B. R/v²
C. v²/R
D. R²/v

Answer: C. v²/R

Very Short Answer Questions

1. Define uniform circular motion.

Uniform circular motion is the motion of an object along a circular path with constant speed.

2. Why is uniform circular motion accelerated motion?

Because the direction of velocity changes continuously.

3. What is centripetal acceleration?

Acceleration directed towards the centre of the circular path is called centripetal acceleration.

4. Write the formula of centripetal acceleration.

a_c = v² / R

5. What is the direction of velocity in circular motion?

Velocity acts along the tangent to the circular path.

Short Answer Questions

1. Explain why velocity changes in uniform circular motion.

In uniform circular motion, speed remains constant but the direction changes continuously. Since velocity depends on both speed and direction, velocity changes continuously.

2. Explain centripetal acceleration.

The acceleration acting on an object moving in a circular path is directed towards the centre of the circle. This acceleration is called centripetal acceleration.

3. Write any two characteristics of uniform circular motion.

1. Speed remains constant.
2. Acceleration acts towards the centre.

4. Differentiate between speed and velocity in uniform circular motion.

Speed	Velocity
Scalar quantity	Vector quantity
Remains constant	Changes continuously

Long Answer Questions

1. Derive the formula for centripetal acceleration.

Consider an object moving with constant speed in a circular path of radius R.

Let velocity at point P be v and at point P′ be v′.

The change in velocity is:

Δv = v′ − v

Acceleration is:

a = Δv / Δt

From similar triangles:

Δv / v = Δr / R

Therefore:

Δv = vΔr / R

Substituting:

a = vΔr / RΔt

For very small time interval:

Δr = vΔt

Therefore:

a = v(vΔt) / RΔt

a_c = v² / R

Thus, centripetal acceleration acts towards the centre of the circle.

Assertion and Reason Questions

1. Assertion (A): Uniform circular motion is accelerated motion.

Reason (R): Velocity changes continuously due to changing direction.

Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

2. Assertion (A): Speed changes continuously in uniform circular motion.

Reason (R): Direction of velocity changes continuously.

Assertion is false but Reason is true.

Fill in the Blanks

1. Uniform circular motion takes place along a ________ path.

circular

2. The acceleration directed towards the centre is called ________ acceleration.

centripetal

3. Velocity in circular motion acts along the ________.

tangent

4. In uniform circular motion, speed remains ________.

constant

Match the Following

Column A	Column B
1. Velocity	a. Towards centre
2. Centripetal acceleration	b. Tangent
3. Uniform circular motion	c. Constant speed
4. Radius	d. Circular path

Answers:
1 → b
2 → a
3 → c
4 → d

Statement-Based Questions

1. Identify true statements:

1. Speed remains constant in UCM.
2. Velocity remains constant in UCM.
3. Acceleration acts towards centre.
4. Velocity acts along tangent.

Statements 1, 3 and 4 are true.

2. Identify the false statement:

A. Speed remains constant
B. Acceleration is zero
C. Velocity changes continuously
D. Motion is circular

B. Acceleration is zero

Case Study Questions

A boy ties a stone to a string and rotates it in a horizontal circular path with constant speed.

1. What type of motion is shown?

Uniform circular motion.

2. Is acceleration present?

Yes, acceleration is present.

3. What is the direction of acceleration?

Towards the centre.

4. What is the direction of velocity?

Along the tangent to the circle.

5. Write the formula of centripetal acceleration.

a_c = v² / R