Physics Circular Motion: Complete Chapter Revision Notes For Class 11 NEET 2027 by PW

Circular Motion is an important Class 11 Physics chapter for NEET because its concepts are directly connected to several mechanics topics studied later. Angular velocity, centripetal acceleration, tangential acceleration, and the relation between linear and angular quantities form the base for understanding many related concepts and solving numerical questions.

The PW Class 11 Circular Motion Complete Chapter One-Shot Video For NEET 2027 covers angular displacement, angular velocity, angular acceleration, their relations, centripetal and tangential acceleration, and uniform and non-uniform circular motion. Building a clear understanding of these concepts can help you handle interconnected topics more confidently during NEET preparation.

Definition Of Circular Motion

When a body moves in a plane such that its distance from a fixed point remains constant, the motion is called circular motion.

• The fixed point is the centre.

• The constant distance from the centre is the radius.

• The body follows a circular path.

Radius Vector

The vector joining the centre of the circle to the moving particle is the radius vector.

Its properties are:

• Magnitude remains constant and equals the radius.

• Direction changes continuously as the particle moves.

Thus, the radius vector has constant magnitude but changing direction.

Circular motion is of two types:

1. Uniform Circular Motion

2. Non-Uniform Circular Motion

Trajectory From Parametric Equations

To identify a trajectory, eliminate time from the equations of (x) and (y).

If:

x = a sin(ωt), y = a cos(ωt)

Squaring and adding gives:

x² + y² = a²(sin²(ωt) + cos²(ωt))

x² + y² = a²

This represents a circle of radius a, centred at the origin. (Memory Tip: Parametric equations containing sine and cosine with the same amplitude often produce x² + y² = constant after squaring and adding.)

For:

x = 4 sin(π/2 − ωt), y = 4 sin(ωt)

use:

sin(π/2 − θ) = cos θ

Then:

x = 4 cos(ωt)

and:

x² + y² = 16

Hence, the path is a circle of radius 4, centred at (0,0). (Memory Tip: The identity sin(π/2 − θ) = cos θ converts the equation into the standard sine-cosine form.)

Linear And Angular Quantities

The quantities θ, ω, and α are axial vectors, directed along the axis of rotation.

For constant angular acceleration:

ω = ω₀ + αt

θ = ω₀t + ½αt²

ω² = ω₀² + 2αθ

Angular displacement during the nth second is:

θₙ = ω₀ + α/2(2n − 1)

These equations apply only when angular acceleration (α) is constant.

Angular Displacement

Angular displacement is the angle through which the position vector rotates during a time interval.

If l is arc length and r is radius:

θ = l/r

or:

l = rθ

The SI unit is the radian. Although angular displacement is dimensionless because it is a ratio of lengths, it is expressed in radians.

One complete revolution equals:

2π rad

For N revolutions:

θ = 2πN

Angular displacement accumulates after every revolution, even when the particle returns to its initial position. For example, 2.5 revolutions produce:

θ = 2.5(2π) = 5π rad

Sense And Direction

• Clockwise and anticlockwise describe the sense of rotation.

• The vector direction is along the axis of rotation.

Using the right-hand rule, curl the fingers in the direction of rotation. The thumb gives the direction of θ vector and ω vector. 

(Memory Tip: Curl the fingers in the direction of rotation; the thumb gives the direction of the angular vector.)

Frequency And Time Period

Frequency is the number of revolutions completed per second:

f = revolutions per second

Time period is the time required for one revolution:

T = 1/f

The SI unit of frequency is s⁻¹, while the SI unit of time period is seconds.

1 RPS = 60 RPM

(Memory Tip: Frequency tells how many revolutions occur in one second; time period tells how much time one revolution takes.)

Angular Velocity And Angular Acceleration

Angular velocity is the rate of change of angular displacement:

ω = dθ/dt

Average angular velocity is:

ω_avg = Δθ/Δt

Angular acceleration is the rate of change of angular velocity:

α = dω/dt = d²θ/dt²

Average angular acceleration is:

α_avg = Δω/Δt

For graphs:

• Slope of θ-t graph = ω

• Slope of ω-t graph = α

• Area under ω-t graph = Δθ

• Area under α-t graph = Δω

The rotational sequence is:

θ → ω → α

Differentiate to move forward and integrate to move backwards.

Important Rotational Conversions

1 revolution = 2π rad

RPM to rad/s = RPM × 2π/60

For example:

120 RPM = 120(2π/60) = 4π rad/s

Minutes must be converted into seconds whenever time is given in minutes.

Linear Velocity And Angular Velocity

The vector relation is:

→v = →ω × →r

Since ω and r are perpendicular:

v = ωr

The radius vector, angular velocity, and linear velocity are mutually perpendicular.

If two particles have equal time periods:

T = 2π/ω

then they have equal angular velocities. Their linear velocities may differ if their radii differ.

Acceleration In Circular Motion

Circular motion has two acceleration components.

Centripetal Acceleration

Centripetal acceleration changes the direction of velocity and points toward the centre:

aC = v²/r = ω²r

It cannot be zero during circular motion.

Tangential Acceleration

Tangential acceleration changes the speed:

aT = d|v⃗|/dt = rα

• Speeding up: aT is in the direction of velocity.

• Slowing down: aT is opposite to velocity.

• Constant speed: aT = 0.

The components are perpendicular, so:

a = √(aC² + aT²)

or:

a = √[(v²/r)² + (rα)²]

Uniform Circular Motion

In Uniform Circular Motion, speed remains constant and equal distances are covered in equal time intervals.

aT = 0

Therefore:

anet = aC

However, velocity, momentum, and acceleration vectors are variable because their directions change continuously.

The angle between velocity and acceleration is:

90°

Also:

→a · →v = 0 

Non-Uniform Circular Motion

In non-uniform circular motion, speed changes, so unequal distances are covered in equal time intervals.

Both accelerations are present:

aC ≠ 0, aT ≠ 0

• Increasing speed:
  a (vector) · v (vector) > 0

• Constant speed:
  a (vector) · v (vector) = 0

• Decreasing speed:
  a (vector) · v (vector) < 0

If speed increases, the angle between a (vector) and v (vector) is acute. If speed decreases, it is obtuse.

When s(t) is given:

v = ds/dt, aT = dv/dt, aC = v²/r

Revise Circular Motion regularly to strengthen your understanding of angular motion, acceleration, and their interconnected concepts. Use the PW Circular Motion Complete Chapter One-Shot Video for NEET 2027 for focused revision and better formula recall. 

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