PYQ Vault

Playbook

Rotational Motion

Moment of inertia feeds torque, angular momentum and rolling. Many of its questions have numeric answers, so learn the standard results and the two axis theorems exactly.

Questions in the bank
168
q/paper in 2025–26
1.64
Numeric answer
44%
Notes pages
8

Tier: Cornerstone

When you’ll see it

A moment of inertia, a centre of mass, a torque about an axis, a spinning body changing shape, or a body rolling on a floor or a slope.

How this chapter is tested

Building a moment of inertia carries a large part of the chapter: from the standard results, the two axis theorems, or by adding and removing parts. Torque, angular momentum and rolling then reuse those values.

Most rolling questions turn on one number, k²/R², fixed by the body's shape. It sets the acceleration down a slope, the speed at the bottom and the split of kinetic energy. Many questions here ask for a number rather than an option.

This is a cornerstone chapter, and it has grown in recent papers. The algebra is short. Marks are lost on the wrong axis, a forgotten piece of mass, or ½mv² written for a body that is also spinning.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Centre of mass and its motion

    Weight each position by its mass; the centre of mass moves as if all the mass and every external force acted there.

  • Rotational kinematics, torque and equilibrium

    Angular equations match straight-line ones with ω in rad/s; τ = r × F; equilibrium needs zero net force and zero net torque.

  • Moment of inertia and radius of gyration

    Standard results for rods, rings, discs and spheres; I = Mk², and a reshaped piece keeps its own mass.

  • Axis theorems and composite bodies

    I = I_cm + Md² from the centre-of-mass axis; I_z = I_x + I_y for flat bodies only; add or remove parts about one axis.

  • Torque, angular acceleration and rotational energy

    τ = Iα about a fixed axis; a spinning body stores ½Iω², which energy conservation trades with height and attached blocks.

  • Angular momentum and its conservation

    L = r × p for a particle, Iω for a body; with no external torque, I₁ω₁ = I₂ω₂.

  • Rolling: velocities and kinetic energy

    v = ωR; the contact point is at rest, the top moves at 2v, and K = ½mv²(1 + k²/R²).

  • Rolling on inclines

    a = g sin θ/(1 + k²/R²) and v² = 2gh/(1 + k²/R²); static friction supplies the spin and does no work.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • The parallel-axis theorem from the wrong axis

    I = I_cm + Md² holds only when one axis passes through the centre of mass. Between two other axes, go back to the centre-of-mass axis first.

  • The removed piece as a point

    Subtracting only m·d² for a hole leaves in its own moment of inertia about its centre. Both must go.

  • ½mv² for a rolling body

    The spin adds ½Iω². Finding v from K = ½mv² overestimates the speed of every rolling body.

  • Kinetic energy kept when bodies stick

    A disc dropped on a spinning disc conserves angular momentum but loses kinetic energy. Equate L, not K.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Rotational Motion notes

Drill every Rotational Motion question

168 questions from the bank, across 8 subtopics.

Drill the 168 questions

Drill one subtopic at a time

The 8 subtopics, in teaching order.

Related playbooks

Often paired with this one — the technique or the trap overlaps. Drill these next.