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.

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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.

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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.

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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.

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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

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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.

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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

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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.

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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.

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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

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11. Parking Condition on a Banked Road

tanθ ≤ μ_s

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

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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)

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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.