Physics · JEE Advanced only

Dynamics of Rigid Bodies with Fixed Axis of Rotation (JEE Advanced)

Not in the JEE Main syllabus, but it is in JEE Advanced. Study time: about 8-12 hours. Spend about 3-4 hours on theory and moment of inertia calculations, 3-4 hours on pulley and constraint problems, and 2-4 hours on energy and angular momentum problems. Practice at least 25-30 problems of varying difficulty..

Last updated: 26 October 2026

Direct answer

Dynamics of rigid bodies with fixed axis of rotation deals with how forces and torques cause rotational motion when an object spins around an axis that does not move.

Dynamics of rigid bodies with fixed axis of rotation deals with how forces and torques cause rotational motion when an object spins around an axis that does not move. You study how moment of inertia, angular acceleration, and torque connect through Newton's second law for rotation. This forms the backbone of problems involving rotating wheels, pulleys, doors, and physical pendulums.

Official syllabus

What the JEE Advanced syllabus says

“Dynamics of rigid bodies with fixed axis of rotation”

Source: JEE Advanced 2026 Information Bulletin, Annexure-I. Closest JEE Main topic: rigid body rotation and equations of rotational motion.

JEE Main focuses mostly on basic rotational kinematics and simple moment of inertia calculations. Advanced goes deeper into combined translation-rotation problems, energy methods for rotating systems, and angular momentum conservation with constraints, which Main-only preparation does not cover thoroughly.

Key ideas

What you must understand

Moment of inertia depends on mass distribution relative to the axis; use parallel and perpendicular axis theorems to shift axes
Torque about the fixed axis equals the rate of change of angular momentum: τ = Iα when I is constant
For systems with multiple bodies (like pulleys with masses), write separate equations for each and connect them using constraints
Rotational kinetic energy is (1/2)Iω² and must be included in energy conservation problems
Angular momentum L = Iω is conserved when net external torque about the axis is zero
Physical pendulum problems require finding the moment of inertia about the pivot and using τ = Iα for small oscillations

Formulas

Formulas and key facts

τ = Iα (Newton's second law for rotation)
L = Iω (angular momentum about fixed axis)
K = (1/2)Iω² (rotational kinetic energy)
I = Σmᵢrᵢ² or I = ∫r²dm (moment of inertia definition)
I = I_cm + Md² (parallel axis theorem)
τ = dL/dt (torque as rate of change of angular momentum)
Work done by torque: W = ∫τ dθ
Power: P = τω

Avoid

Common mistakes

Forgetting to use the moment of inertia about the actual axis of rotation, not the center of mass
Ignoring the rotational inertia of pulleys when the problem says the pulley has mass
Sign errors when setting up torque equations: clockwise and anticlockwise torques must be handled consistently
Using v = rω incorrectly when the point is not on the rim or when the constraint is different

Worked example

A JEE Advanced-level example

Question. A uniform solid cylinder of mass M = 4 kg and radius R = 0.2 m can rotate freely about its horizontal axis. A light string is wound around the cylinder, and a block of mass m = 2 kg hangs from the string. The system is released from rest. Find the acceleration of the block and the tension in the string. (Take g = 10 m/s²)

Show solution

For the block: mg - T = ma, so 2(10) - T = 2a, giving 20 - T = 2a
For the cylinder: Torque = TR, and I = (1/2)MR² = (1/2)(4)(0.04) = 0.08 kg·m². Using τ = Iα: TR = 0.08 × α
Constraint: a = Rα, so α = a/R = a/0.2 = 5a. Substituting: T(0.2) = 0.08 × 5a, giving 0.2T = 0.4a, so T = 2a
Substitute T = 2a into the block equation: 20 - 2a = 2a, so 20 = 4a, giving a = 5 m/s²
Find tension: T = 2a = 2(5) = 10 N

Answer: Acceleration of block = 5 m/s², Tension in string = 10 N

Solved twice independently; both solutions agree.

FAQs

Frequently asked questions

Is Dynamics of Rigid Bodies with Fixed Axis of Rotation in the JEE Main syllabus?

No. It is in the JEE Advanced 2026 syllabus only. The closest JEE Main topic is rigid body rotation and equations of rotational motion.

How long does Dynamics of Rigid Bodies with Fixed Axis of Rotation take to prepare for JEE Advanced?

About 8-12 hours. Spend about 3-4 hours on theory and moment of inertia calculations, 3-4 hours on pulley and constraint problems, and 2-4 hours on energy and angular momentum problems. Practice at least 25-30 problems of varying difficulty., if you already know the related JEE Main topic.