Circular Motion Class 11 Physics Notes | CBSE & NEET Complete Guide

NEET Circular Motion Chapter Explained | Class 11 Physics Study Material

 - Dr.Sanjaykumar Pawar 

Circular Motion in Physics: Centripetal force keeps objects moving in a circular path towards the center.

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NEET Physics Notes - Circular Motion

1. What is Circular Motion?

Circular motion is the motion of an object along a circular path.

Examples:

• Stone tied to a string and rotated.
• Car taking a circular turn.
• Planet revolving around the Sun.
• Satellite moving around Earth.

---

2. Centripetal Acceleration

While moving in a circle, the direction of velocity continuously changes. Therefore the object experiences acceleration.

This acceleration is directed towards the centre of the circular path and is called Centripetal Acceleration.

a_c = v² / R

Where:

• a_c = Centripetal acceleration
• v = Speed of object
• R = Radius of circular path

Direction of centripetal acceleration is always towards the centre.

---

3. Centripetal Force

According to Newton's Second Law:

F = ma

Since acceleration is centripetal acceleration:

F_c = mv² / R

Where:

• F_c = Centripetal force
• m = Mass of object
• v = Speed
• R = Radius of circular path

The force acting towards the centre of a circular path is called Centripetal Force.

---

4. Sources of Centripetal Force

Situation	Centripetal Force Provided By
Stone tied to string	Tension in string
Planet around Sun	Gravitational force
Satellite around Earth	Gravitational force
Car taking a turn	Friction force

Centripetal force is not a separate force. It is provided by existing forces such as tension, gravity or friction.

---

5. Motion of a Car on a Level Road

Forces Acting on the Car

• Weight (mg) acting downward.
• Normal reaction (N) acting upward.
• Friction force (f) acting towards the centre.

Vertical Equilibrium

N - mg = 0

N = mg

Since there is no vertical acceleration, normal reaction balances the weight.

Centripetal Force Provided by Friction

f = mv² / R

Maximum static friction:

f = μ_sN

Since N = mg

f = μ_smg

For safe turning:

mv² / R ≤ μ_smg

v² ≤ μ_sRg

---

6. Maximum Speed on a Level Road

v_max = √(μ_sRg)

Where:

• μ_s = Coefficient of static friction
• R = Radius of circular path
• g = Acceleration due to gravity

Observations

• Maximum speed is independent of mass.
• Greater friction gives greater safe speed.
• Larger radius allows larger speed.
• If speed exceeds v_max, car skids outward.

---

7. Motion of a Car on a Banked Road

A banked road is a road whose outer edge is raised above the inner edge.

The road makes an angle θ with the horizontal.

Advantages of Banking

• Reduces dependence on friction.
• Allows safe turning at higher speed.
• Reduces chances of skidding.

Forces Acting

• Weight (mg)
• Normal reaction (N)
• Friction force (f)

Vertical Force Equation

N cosθ = mg + f sinθ

Horizontal Force Equation

N sinθ + f cosθ = mv² / R

---

8. Maximum Speed on a Banked Road

For maximum speed:

f = μ_sN

The final formula becomes:

v_max = √[ Rg (tanθ + μ_s) / (1 - μ_stanθ) ]

Maximum speed on a banked road is greater than on a level road.

---

9. Ideal Banking (No Friction Required)

When friction is not required:

μ_s = 0

The design speed becomes:

v₀ = √(Rg tanθ)

At Design Speed

• Friction is zero.
• Tyre wear is minimum.
• Driving is smoother.
• Road is safest.

---

10. Direction of Friction on Banked Road

Condition	Direction of Friction
v = v₀	No friction required
v < v₀	Up the slope
v > v₀	Down the slope

---

11. Parking Condition on a Banked Road

tanθ ≤ μ_s

This condition ensures that the vehicle does not slide down the banked road.

---

12. Important NEET Formulas

Quantity	Formula
Centripetal Acceleration	ac = v²/R
Centripetal Force	Fc = mv²/R
Maximum Speed on Level Road	vmax = √(μsRg)
Design Speed on Banked Road	v0 = √(Rg tanθ)

---

13. NEET Quick Revision

• Circular motion requires centripetal force.
• Centripetal force always acts towards the centre.
• Centripetal acceleration = v²/R.
• Centripetal force = mv²/R.
• Friction provides centripetal force on level roads.
• Maximum speed on level road = √(μ_sRg).
• Banking helps vehicles take turns safely.
• Ideal banking speed = √(Rg tanθ).
• At ideal speed, friction is not required.
• Maximum speed on a banked road is greater than on a flat road.

Circular Motion - Mind Map (NEET)

CIRCULAR MOTION
│
├── Definition
│   ├── Motion along a circular path
│   ├── Direction changes continuously
│   └── Velocity changes even if speed is constant
│
├── Centripetal Acceleration
│   │
│   ├── Acts towards centre
│   ├── Responsible for circular motion
│   └── Formula
│       └── ac = v²/R
│
├── Centripetal Force
│   │
│   ├── Force towards centre
│   ├── Keeps object in circular path
│   └── Formula
│       └── Fc = mv²/R
│
├── Sources of Centripetal Force
│   │
│   ├── Stone on string
│   │   └── Tension
│   │
│   ├── Planet around Sun
│   │   └── Gravitational Force
│   │
│   ├── Satellite around Earth
│   │   └── Gravitational Force
│   │
│   └── Car on curved road
│       └── Friction
│
├── Car on Level Road
│   │
│   ├── Forces Acting
│   │   ├── Weight (mg)
│   │   ├── Normal Reaction (N)
│   │   └── Friction (f)
│   │
│   ├── Vertical Equilibrium
│   │   └── N = mg
│   │
│   ├── Centripetal Force
│   │   └── Provided by Friction
│   │
│   └── Maximum Speed
│       └── vmax = √(μsRg)
│
├── Important Observations
│   │
│   ├── vmax independent of mass
│   ├── Higher friction → Higher speed
│   ├── Larger radius → Higher speed
│   └── Exceed vmax → Car skids outward
│
├── Banked Road
│   │
│   ├── Outer edge raised
│   ├── Angle of banking = θ
│   ├── Reduces dependence on friction
│   └── Allows higher speed turns
│
├── Forces on Banked Road
│   │
│   ├── Weight (mg)
│   ├── Normal Reaction (N)
│   └── Friction (f)
│
├── Maximum Speed on Banked Road
│   │
│   └── vmax =
│       √[Rg(tanθ + μs)/(1 − μstanθ)]
│
├── Ideal Banking
│   │
│   ├── μs = 0
│   ├── No friction required
│   ├── Smooth driving
│   └── Design Speed
│       └── v0 = √(Rg tanθ)
│
├── Friction Direction
│   │
│   ├── v = v0
│   │   └── No friction
│   │
│   ├── v < v0
│   │   └── Friction up the slope
│   │
│   └── v > v0
│       └── Friction down the slope
│
├── Parking Condition
│   │
│   └── tanθ ≤ μs
│
└── NEET Formula Revision
    │
    ├── ac = v²/R
    ├── Fc = mv²/R
    ├── vmax(level) = √(μsRg)
    ├── v0 = √(Rg tanθ)
    └── Centripetal force → Always towards centre

CIRCULAR MOTION - COMPLETE QUESTION BANK (CLASS 11 CBSE)

1. Multiple Choice Questions (MCQs)

Q1. The direction of centripetal force is:
a) Tangential
b) Away from centre
c) Towards centre
d) Upward

Answer: c) Towards centre

Q2. Formula of centripetal force is:

Answer: F = mv²/R

Q3. In circular motion, speed remains constant but:

Answer: Velocity changes due to change in direction.

Q4. Maximum speed on a level road depends on:

Answer: μs, R and g

Q5. Banking of roads reduces:

Answer: Dependence on friction

2. Very Short Answer Questions

Q1. Define centripetal acceleration.

Answer: Acceleration directed towards the centre in circular motion.

Q2. Write formula of centripetal acceleration.

Answer: a = v²/R

Q3. Give one example of circular motion.

Answer: Motion of a stone tied to a string.

Q4. Which force provides centripetal force in planets?

Answer: Gravitational force.

3. Short Answer Questions

Q1. Why is friction necessary for a car on a circular road?

Because friction provides the centripetal force required to keep the car moving in a circular path.

Q2. Why does a passenger feel outward push during turning?

Due to inertia, the body tends to move in a straight line while the car turns.

Q3. What is banking of roads?

Raising the outer edge of a curved road above the inner edge.

4. Long Answer Questions

Q1. Derive maximum speed on a level road.

Centripetal force = mv²/R
Friction = μs mg
So mv²/R ≤ μs mg
v² ≤ μs R g
vmax = √(μs R g)

Q2. Explain ideal banking.

When no friction is required to take a turn on a banked road.
v = √(Rg tanθ)

5. Assertion & Reason

A: Centripetal force acts towards centre.
R: It changes direction of velocity.

Answer: Both A and R are true and R is correct explanation.

A: Maximum speed depends on mass.
R: Friction depends on mass.

Answer: A is false, R is true.

6. Fill in the Blanks

1. Centripetal force always acts towards ______.

Answer: centre

2. Centripetal acceleration is perpendicular to ______.

Answer: velocity

3. Maximum speed on level road = ______.

Answer: √(μsRg)

7. Match the Following

Column A	Column B
Planet around Sun	Gravity
Car on road	Friction
Stone in string	Tension

8. Case Study

A car of mass 1000 kg moves on a circular road of radius 50 m. μs = 0.4, g = 10 m/s².

Q1. Which force provides centripetal force?

Answer: Friction

Q2. Find vmax.

v = √(μs R g)
= √(0.4 × 50 × 10)
= √200 = 14.14 m/s

Q3. What happens if speed increases?

Answer: Car will skid outward.

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