Q1. A disc of moment of inertia 0.5 kg·m² spins at 20 rad/s. Find its rotational kinetic energy.
KE = ½ I ω²
KE = ½ × 0.5 × 20²
KE = 100 J
System of Particles and Rotational Motion — Class 11
Rotation is the twin of straight-line motion. Learn torque, moment of inertia and angular momentum, and compute torque instantly.
Centre of massThe point where the whole mass of a system can be taken to be concentrated; it moves as if all external force acts there.
TorqueThe turning effect of a force, τ = r·F·sinθ = rF₊ (perpendicular force × distance). The rotational analogue of force.
Moment of inertia (I)A body's resistance to angular acceleration, I = Σmr². The rotational analogue of mass; depends on the axis.
Angular momentumL = Iω, conserved when no external torque acts (why a spinning skater speeds up on pulling in their arms).
Torque calculator Interactive
Find the torque of a force applied at a distance from the axis, at any angle.
Torque, τ = rF·sinθ—N·m
Torque is maximum when the force is perpendicular to the arm (θ = 90°) — that is why you push a door at its edge.
Numericals practice Interactive
Torque and angular-momentum problems with steps.
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Solved numericals
Q2. Why does a spinning ice-skater speed up on pulling in their arms?
No external torque acts, so angular momentum L = Iω is conserved.
Pulling arms in reduces the moment of inertia I.
To keep L constant, ω (spin rate) must increase.
Formula sheet
| Quantity | Formula | SI unit |
|---|---|---|
| Torque | τ = r F sinθ | N·m |
| Newton's 2nd law (rotation) | τ = I α | N·m |
| Angular momentum | L = I ω | kg·m²/s |
| Rotational KE | KE = ½ I ω² | J |
| Moment of inertia (point) | I = m r² | kg·m² |
Common mistakes & exam wins
- Torque τ = rF sinθ is maximum when the force is perpendicular to the arm.
- Moment of inertia depends on the axis and how mass is distributed, not just the total mass.
- Angular momentum L = Iω is conserved when net external torque is zero.
- Rotational quantities mirror linear ones: F→τ, m→I, v→ω, p→L.
Frequently asked questions
What is torque?
The turning effect of a force about an axis, τ = rF sinθ, measured in newton-metres.
What is moment of inertia?
A body's resistance to changes in its rotational motion, I = Σmr²; it is the rotational analogue of mass.
When is angular momentum conserved?
When the net external torque on a system is zero — then L = Iω stays constant.