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Circular Motion Notes Class 11 for CBSE, JEE and NEET: Formulas, Banking, Vertical Circle and Solved Examples

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eSaral Academic and Editorial Team

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Summary

Circular motion notes Class 11 cover uniform and non-uniform circular motion, angular velocity, centripetal acceleration and force, motion on a level and banked road, and motion in a vertical circle. This page gives the key formulas, a centripetal vs centrifugal comparison, solved examples and handwritten notes for CBSE, JEE and NEET.

Circular Motion Notes Class 11th - IIT JEE

Circular motion is a topic that is spread over three chapters of Class 11 Physics, so students often miss a part of it. These circular motion notes Class 11 put the whole topic in one place, from definitions to the vertical circle, and they follow the current NCERT chapter order.

Circular Motion Notes Class 11: Where Does It Fit in the Syllabus?

Part of circular motion

NCERT Class 11 Physics chapter

Uniform circular motion, angular velocity, centripetal acceleration

Chapter 3: Motion in a Plane

Dynamics of circular motion, centripetal force, motion of a vehicle on a level and a banked road

Chapter 4: Laws of Motion

Motion in a vertical circle

Chapter 5: Work, Energy and Power

Non-uniform circular motion (with tangential acceleration) goes beyond the NCERT text, but it is useful for JEE.

What Is Circular Motion? Core Definitions in Circular Motion Notes Class 11

Circular motion is the motion of a body along a circular path. The speed may be constant (uniform circular motion) or may change (non-uniform circular motion). In both cases, the direction of the velocity changes continuously, so there is always an acceleration, even when the speed is constant.

The changing direction of velocity is easier to understand after you review vectors in plane motion, where both magnitude and direction are treated explicitly.

Uniform and Non-Uniform Circular Motion

Feature

Uniform circular motion

Non-uniform circular motion

Speed

Constant

Changes with time

Tangential acceleration

Zero

Not zero (a_t = dv/dt)

Centripetal acceleration

v²/r, constant in magnitude

v²/r, changes with speed

Net acceleration

Towards the centre

Has a centripetal and a tangential part

Angular velocity

Constant

Changes (angular acceleration α ≠ 0)

Key Formulas in Circular Motion Notes Class 11

Quantity

Formula

Notes

Angular displacement

θ = s/r

In radians

Angular velocity

ω = dθ/dt

In rad/s

Relation between speed and angular velocity

v = rω


Time period and frequency

T = 2π/ω = 2πr/v, f = 1/T

ω = 2πf

Centripetal acceleration

a_c = v²/r = ω²r

Directed towards the centre

Centripetal force

F_c = mv²/r = mω²r

Not a new force. It is the net force towards the centre.

Angular acceleration

α = dω/dt


Tangential acceleration

a_t = dv/dt = rα

Along the tangent

Net acceleration

a = √(a_c² + a_t²)

For non-uniform circular motion

Centripetal Force vs Centrifugal Force in Circular Motion Notes Class 11

Feature

Centripetal force

Centrifugal force

Nature

A real net force

A pseudo-force

Direction

Towards the centre

Away from the centre

Frame of reference

Inertial (ground) frame

Rotating (non-inertial) frame

Provided by

Tension, gravity, friction, normal force or a combination

Appears only because the frame is accelerating

When you solve a problem from the ground frame, do not add a centrifugal force. Write F_net towards the centre = mv²/r.

Circular Motion on a Horizontal Plane: Circular Motion Notes Class 11

Vehicle on a Level Circular Road

Friction provides the centripetal force. The maximum safe speed is v_max = √(μrg), where μ is the coefficient of friction and r is the radius of the turn.

Banking of Roads

On a road banked at angle θ, a component of the normal force also provides the centripetal force. For a vehicle that needs no friction (the ideal speed), tan θ = v²/(rg). With friction, the maximum safe speed is v² = rg (tan θ + μ)/(1 − μ tan θ).

Conical Pendulum

A bob of mass m moves in a horizontal circle with the string making angle θ with the vertical. The conditions are tan θ = v²/(rg), and the time period is T = 2π√(L cos θ / g), where L is the string length.

Motion in a Vertical Circle: Circular Motion Notes Class 11

In a vertical circle, the speed changes because gravity does work, so the motion is non-uniform. Use energy conservation between two points, and Newton’s second law towards the centre at each point.

Case

Minimum speed at the top

Minimum speed at the bottom

Mass on a string (the string must stay taut)

√(gr)

√(5gr)

Mass on a light rod or inside a tube

0

√(4gr)

For a mass on a string:

  • Tension at the top: T_top = mv²/r − mg
  • Tension at the bottom: T_bottom = mv²/r + mg
  • The difference in tension between the bottom and the top, for a complete circle, is 6mg.

For a vehicle on the top of a convex bridge, N = mg − mv²/r, so the vehicle loses contact with the road when v = √(gr). To go deeper into the energy method, read eSaral’s Work, Energy and Power Class 11 notes.

Solved Examples from Circular Motion Notes Class 11

Example 1 (level road): A car goes round a level circular road of radius 50 m. The coefficient of friction is 0.5. Find the maximum speed (g = 10 m/s²).

v_max = √(μrg) = √(0.5 × 50 × 10) = √250 ≈ 15.8 m/s, which is about 57 km/h.

Example 2 (banking): A road of radius 100 m is to be banked so that a vehicle can take a turn at 20 m/s without friction. Find the angle of banking (g = 10 m/s²).

tan θ = v²/(rg) = 400/(100 × 10) = 0.4, so θ ≈ 21.8°.

Example 3 (vertical circle): A stone of mass 0.1 kg is tied to a 0.4 m string and whirled in a vertical circle. Find the minimum speed at the bottom to complete the circle, and the difference in tension between the bottom and the top (g = 10 m/s²).

v_bottom = √(5gr) = √(5 × 10 × 0.4) = √20 ≈ 4.5 m/s. The tension difference is 6mg = 6 × 0.1 × 10 = 6 N.

Example 4 (centripetal acceleration): A point on a wheel of radius 0.5 m rotates at 120 revolutions per minute. Find its centripetal acceleration.

ω = 2π × 120/60 = 4π rad/s ≈ 12.57 rad/s. a_c = ω²r = (12.57)² × 0.5 ≈ 79 m/s².

Circular Motion Notes Class 11: Handwritten Notes

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

India's Best Exam Preparation for Class 11th - Download Now

Common Mistakes in Circular Motion Notes Class 11 Problems

Mistake

Correct approach

Treating centripetal force as an extra force on the free-body diagram

Draw only real forces, and then write that their net force towards the centre equals mv²/r

Adding centrifugal force in a ground-frame solution

Use centrifugal force only if you solve in the rotating frame

Using √(gr) at the bottom of a vertical circle

√(gr) is the minimum speed at the top. At the bottom it is √(5gr) for a string.

Using the string condition for a rod

For a rod or tube, the minimum speed at the top is zero, and at the bottom it is √(4gr)

Forgetting tangential acceleration in non-uniform motion

The net acceleration has both a centripetal and a tangential part

What Do CBSE, JEE and NEET Ask from Circular Motion Notes Class 11 Topics?

  • CBSE: definitions, a_c and F_c formulas, banking of roads and simple numericals.
  • JEE Main and JEE Advanced: vertical circle conditions, conical pendulum, banking with friction and non-uniform circular motion.
  • NEET: uniform circular motion, centripetal force, banking and the vertical circle, in numerical form.

The number of questions varies each year, so use previous year questions to see the trend.

Frequently Asked Questions

What are the most important topics in circular motion notes Class 11 for JEE Main?

In the circular motion notes Class 11, centripetal force and acceleration, motion in a vertical circle (minimum speed conditions), banking of roads, and the conical pendulum are the most important topics. Master the force diagrams and the energy conservation approach for each, and practise previous year questions.

What is the difference between centripetal and centrifugal force?

Centripetal force is a real net force directed towards the centre of the path, and it is provided by tension, gravity, friction or the normal force. Centrifugal force is a pseudo-force that appears only in a rotating (non-inertial) frame and acts away from the centre. When you solve from the ground frame, you do not use it.

What is the minimum speed required to complete a vertical circle?

In circular motion notes Class 11, for a mass on a string, the minimum speed at the top is √(gr), and the minimum speed at the bottom is √(5gr). For a mass on a light rod or in a tube, the speed at the top can be zero, and the minimum speed at the bottom is √(4gr).

How is banking of roads related to circular motion?

In circular motion notes Class 11, banking tilts the road so that a component of the normal force provides part of the centripetal force, which reduces the friction needed to take a turn. For no friction at the ideal speed, tan θ = v²/(rg), where v is the speed and r is the radius of the turn.

Where does circular motion come in the Class 11 Physics NCERT book?

The topic is spread across three chapters: uniform circular motion in Chapter 3 (Motion in a Plane), centripetal force and banking in Chapter 4 (Laws of Motion), and the vertical circle in Chapter 5 (Work, Energy and Power). These circular motion notes Class 11 on eSaral bring them together.

Is circular motion in Class 11 Physics important for NEET?

Yes. NEET Physics includes questions on uniform circular motion, centripetal force and banking. The number of questions changes from year to year, so check previous years’ NEET papers. The same circular motion notes Class 11 serve JEE and NEET.

What is the formula for centripetal acceleration?

In circular motion notes Class 11, centripetal acceleration is a_c = v²/r = ω²r, and it is directed towards the centre of the circle. For uniform circular motion, it is the only acceleration.

Can there be acceleration in uniform circular motion?

Yes. The speed is constant, but the direction of the velocity changes continuously, so the velocity changes, and this gives a centripetal acceleration towards the centre.

What is the difference between uniform and non-uniform circular motion?

In uniform circular motion, the speed is constant and the only acceleration is centripetal. In non-uniform circular motion, the speed changes, so there is also a tangential acceleration, and the net acceleration is √(a_c² + a_t²).

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Team eSaral

eSaral Academic and Editorial Team

Team eSaral is the collective author profile for educational content created by eSaral’s teachers and academic contributors. The team draws on expertise from IIT graduates, doctors, experienced educators and subject specialists to develop resources for JEE, NEET and school students. Our articles aim to explain concepts clearly and help students study with confidence.

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