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If you live in Downtown Dubai and you are searching for a good Physics Tutor in Downtown Dubai, then Kumar Physics Classes can help you learn Physics in a simple, clear and result-oriented way.

Downtown Dubai is one of the most premium and important areas of Dubai. Many students living in and around Downtown Dubai study in CBSE schools, IB schools, British curriculum schools, A-Level programs, IGCSE programs, AP Physics courses, NEET preparation and IIT JEE preparation. But many students face one common problem: Physics looks easy in theory, but it becomes difficult when numerical questions, derivations, graphs and conceptual applications come.

If you are not able to understand rotational motion, torque, angular momentum, moment of inertia, rolling motion, gravitation, electrostatics, current electricity, magnetism, optics or modern physics, then you can connect with Kumar Sir for online Physics classes.

Kumar Sir teaches Physics from basic to advanced level. His style is simple: first concept clarity, then formula understanding, then derivation, then numerical practice, and finally exam-level questions.

Physics Tutor in Downtown Dubai for CBSE, IB, IGCSE, A-Level, AP, NEET and IIT JEE

At Kumar Physics Classes, students can study:

CBSE Class 11 Physics
CBSE Class 12 Physics
IB Physics SL and HL
IGCSE Physics
A-Level Physics
British Curriculum Physics
AP Physics 1
AP Physics 2
AP Physics C Mechanics
AP Physics C Electricity and Magnetism
NEET Physics
IIT JEE Main Physics
IIT JEE Advanced Physics

If you are living in Downtown Dubai and your Physics concepts are weak, then online classes with Kumar Sir can help you build strong fundamentals.

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Rotational Motion Class 11 Physics Formula Sheet

Rotational Motion is one of the most important chapters of Class 11 Physics. It is very useful for CBSE, NEET, IIT JEE, AP Physics and A-Level Physics. Students must understand this chapter properly because many questions are based on torque, angular momentum, moment of inertia, rolling motion and conservation laws.

1. Angular Displacement

Angular displacement is the angle rotated by a body.

Formula:

θ = s / r

Where:

θ = angular displacement
s = arc length
r = radius

Unit of angular displacement is radian.

2. Angular Velocity

Angular velocity is the rate of change of angular displacement.

Formula:

ω = dθ / dt

For uniform circular motion:

ω = 2π / T

ω = 2πf

Where:

ω = angular velocity
T = time period
f = frequency

3. Angular Acceleration

Angular acceleration is the rate of change of angular velocity.

Formula:

α = dω / dt

Unit:

rad/s²

4. Relation Between Linear and Angular Quantities

v = rω

aₜ = rα

a꜀ = rω²

a꜀ = v² / r

Where:

v = linear velocity
r = radius
ω = angular velocity
α = angular acceleration
aₜ = tangential acceleration
a꜀ = centripetal acceleration

5. Equations of Rotational Motion

For constant angular acceleration:

ω = ω₀ + αt

θ = ω₀t + 1/2 αt²

ω² = ω₀² + 2αθ

θ = [(ω + ω₀) / 2] t

These are similar to linear motion equations.

6. Torque

Torque is the turning effect of force.

Vector form:

τ⃗ = r⃗ × F⃗

Magnitude:

τ = rF sinθ

Also:

τ = Force × perpendicular distance

Unit:

N m

Torque is a vector quantity.

7. Moment of Inertia

Moment of inertia is the rotational inertia of a body.

For particles:

I = Σmr²

For continuous body:

I = ∫r² dm

Moment of inertia depends on:

Mass of body
Distribution of mass
Axis of rotation

8. Rotational Kinetic Energy

K = 1/2 Iω²

For rolling body:

K total = 1/2 Mv² + 1/2 Iω²

9. Angular Momentum

Angular momentum is rotational momentum.

For a particle:

L⃗ = r⃗ × p⃗

Magnitude:

L = mvr sinθ

For a rigid body rotating about a fixed axis:

L = Iω

10. Relation Between Torque and Angular Momentum

τ⃗ = dL⃗ / dt

This is one of the most important formulas in rotational motion.

When is Angular Momentum Conserved?

Angular momentum is conserved when net external torque on the system is zero.

τ external = 0

Then:

dL / dt = 0

So:

L = constant

For a rotating body:

Iω = constant

This means if moment of inertia decreases, angular velocity increases. If moment of inertia increases, angular velocity decreases.

Kumar Sir Style Explanation

Suppose a student is sitting on a rotating chair with hands stretched out. When the student pulls the hands inward, moment of inertia decreases. Since angular momentum is conserved, angular velocity increases. That is why the student rotates faster.

So remember:

I₁ω₁ = I₂ω₂

This formula is used when there is no external torque.

When Torque is Constant

If torque is constant, angular acceleration is also constant, because:

τ = Iα

If I is constant, then:

α = τ / I

So when torque is constant, we can use rotational equations of motion:

ω = ω₀ + αt

θ = ω₀t + 1/2 αt²

ω² = ω₀² + 2αθ

Also, from torque and angular momentum:

τ = dL / dt

If torque is constant:

L = L₀ + τt

So constant torque means angular momentum changes uniformly with time.

Important point:

If torque is zero, angular momentum is conserved.
If torque is constant, angular momentum changes at a constant rate.

11. Work Done by Torque

W = τθ

For variable torque:

W = ∫τ dθ

12. Power in Rotational Motion

P = τω

13. Radius of Gyration

I = Mk²

k = √(I / M)

Where k is radius of gyration.

14. Parallel Axis Theorem

I = Icm + Md²

Where:

I = moment of inertia about new axis
Icm = moment of inertia about centre of mass axis
M = mass
d = distance between two parallel axes

15. Perpendicular Axis Theorem

For a plane lamina:

Iz = Ix + Iy

This theorem is valid only for plane lamina.

Important Moment of Inertia Formulas

Uniform Ring

About centre, perpendicular to plane:

I = MR²

About diameter:

I = 1/2 MR²

Uniform Disc

About centre, perpendicular to plane:

I = 1/2 MR²

About diameter:

I = 1/4 MR²

Solid Sphere

About diameter:

I = 2/5 MR²

Hollow Sphere

About diameter:

I = 2/3 MR²

Rod

About centre, perpendicular to length:

I = 1/12 ML²

About end, perpendicular to length:

I = 1/3 ML²

Cylinder

Solid cylinder about its axis:

I = 1/2 MR²

Hollow cylinder about its axis:

I = MR²

Rolling Motion Formulas

For pure rolling:

v = Rω

a = Rα

Total kinetic energy:

K = 1/2 Mv² + 1/2 Iω²

If:

I = Mk²

Then:

K = 1/2 Mv² (1 + k²/R²)

Acceleration of Rolling Body on Inclined Plane

General formula:

a = g sinθ / (1 + I / MR²)

For ring:

a = g sinθ / 2

For disc:

a = (2/3) g sinθ

For solid sphere:

a = (5/7) g sinθ

For hollow sphere:

a = (3/5) g sinθ

Why Rotational Motion is Difficult for Students

Rotational Motion is difficult because students try to memorise formulas without understanding the meaning of torque, angular momentum and moment of inertia.

Kumar Sir explains this chapter in a simple way:

Force produces linear acceleration.
Torque produces angular acceleration.
Mass resists linear motion.
Moment of inertia resists rotational motion.
Linear momentum is mv.
Angular momentum is Iω.
Work in linear motion is Fs.
Work in rotational motion is τθ.

Once students understand this comparison, rotational motion becomes easy.

Why Choose Kumar Physics Classes?

Students in Downtown Dubai can choose Kumar Physics Classes because:

30+ years teaching experience
Strong concept clarity
Step-by-step derivations
Numerical problem solving
Board and competitive exam focus
CBSE, IB, IGCSE, A-Level, AP, NEET and IIT JEE support
Online classes from India
Personal attention
Doubt clearing
Regular assignments
Friendly explanation style

Kumar Sir believes that Physics becomes easy when concepts are clear.

Contact Kumar Physics Classes

For online Physics classes from Downtown Dubai, contact:

Kumar Physics Classes
Website: kumarphysicsclasses.com
Phone: +91-9958461445
Email: kumarsirphysics@gmail.com

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25 Conceptual Questions on Rotational Motion

1. What is torque?

Answer:
Torque is the turning effect of force. If force tries to rotate a body about an axis, then that effect is called torque.

Formula:
τ = rF sinθ

2. Why is torque zero when force passes through the axis of rotation?

Answer:
Because perpendicular distance from axis becomes zero. If distance is zero, turning effect is zero.

Formula:
τ = Force × perpendicular distance

3. Does a larger force always produce larger torque?

Answer:
No. Torque depends on force and perpendicular distance. A smaller force applied far from the axis can produce more torque.

4. Why is it easier to open a door by pushing near the handle?

Answer:
Because handle is far from the hinge. Distance from axis is large, so torque becomes large.

5. What is angular momentum?

Answer:
Angular momentum is the rotational form of linear momentum.

For a rotating body:
L = Iω

For a particle:
L = mvr sinθ

6. When is angular momentum conserved?

Answer:
Angular momentum is conserved when net external torque on the system is zero.

If τ external = 0, then L = constant.

7. Why does a skater rotate faster when hands are pulled inward?

Answer:
When hands are pulled inward, moment of inertia decreases. Since angular momentum is conserved, angular velocity increases.

Formula:
I₁ω₁ = I₂ω₂

8. Can angular momentum change if torque is zero?

Answer:
No. If net external torque is zero, angular momentum remains constant.

9. What happens when torque is constant?

Answer:
If torque is constant, angular momentum changes uniformly with time.

Formula:
τ = dL/dt

So:
L = L₀ + τt

10. What is moment of inertia?

Answer:
Moment of inertia is the rotational inertia of a body. It tells how difficult it is to rotate a body.

Formula:
I = Σmr²

11. Does moment of inertia depend only on mass?

Answer:
No. It depends on mass and distribution of mass from the axis of rotation.

12. Why does a ring have more moment of inertia than a disc of same mass and radius?

Answer:
In a ring, all mass is at distance R from the axis. In a disc, mass is spread from centre to radius R. So ring has larger moment of inertia.

Ring:
I = MR²

Disc:
I = 1/2 MR²

13. Why is moment of inertia called rotational mass?

Answer:
Because mass resists linear motion, and moment of inertia resists rotational motion.

14. What is radius of gyration?

Answer:
Radius of gyration is the distance from the axis where whole mass can be assumed to be concentrated to give the same moment of inertia.

Formula:
I = Mk²

15. What is parallel axis theorem?

Answer:
Parallel axis theorem gives moment of inertia about any axis parallel to the centre of mass axis.

Formula:
I = Icm + Md²

16. Why does moment of inertia increase in parallel axis theorem?

Answer:
Because the new axis is away from centre of mass. Distance d adds extra rotational inertia Md².

17. Can parallel axis theorem be applied to any body?

Answer:
Yes, it can be applied to any rigid body, but the two axes must be parallel.

18. What is perpendicular axis theorem?

Answer:
For a plane lamina, moment of inertia about an axis perpendicular to its plane is equal to the sum of moments of inertia about two perpendicular axes in the plane.

Formula:
Iz = Ix + Iy

19. Is perpendicular axis theorem valid for solid sphere?

Answer:
No. It is valid only for plane lamina, not for 3D solid bodies.

20. Why is perpendicular axis theorem useful for disc and ring?

Answer:
Because disc and ring are plane bodies. We can find moment of inertia about diameter using moment of inertia about central perpendicular axis.

21. What are equations of rotational motion?

Answer:
For constant angular acceleration:

ω = ω₀ + αt

θ = ω₀t + 1/2 αt²

ω² = ω₀² + 2αθ

θ = [(ω + ω₀)/2]t

22. When can we use rotational equations of motion?

Answer:
We can use them only when angular acceleration is constant.

23. What is the relation between torque and angular acceleration?

Answer:
Torque produces angular acceleration.

Formula:
τ = Iα

This is rotational form of F = ma.

24. What is the difference between linear and rotational motion?

Answer:
In linear motion, body moves along a straight or curved path. In rotational motion, body rotates about an axis.

Linear:
F = ma

Rotational:
τ = Iα

25. Why is rotational motion important in Physics?

Answer:
Because many real-life systems rotate, like wheels, fans, planets, gears and pulleys. Rotational motion helps us understand torque, angular momentum, rolling motion and mechanical systems.