Playbook
Rotational Dynamics
128 q - 3.13/paper - 21% HARD, and rising in 2025. The axis theorems hold nearly half the HARD; angular momentum and rolling are the cheap pages.
- Questions in the bank
- 128
- q/paper (2024–25 papers)
- 3.13
- Tagged HARD
- 21%
- Subtopics
- 6
Strand: Cornerstone
When you’ll see it
A moment of inertia, a body rolling down a slope, a spinning body changing shape, or anything moving in a circle — banked roads, conical pendulums, vertical circles.
How this chapter is tested
128 q at 3.13 a paper, and rising: 2.89 a paper across 2023-24, then 3.38 across 2025. It is 21% HARD, and nearly half of that HARD sits on one page — Parallel and Perpendicular Axis Theorems, 25 questions at 48%.
The cheap pages are the conservation laws. Angular Momentum, Torque, and Conservation is 22 questions at 5% HARD: a skater pulls in her arms, I falls, ω rises so that Iω stays fixed. Rotational Kinetic Energy and Rolling Motion is 24 questions at 8%, and one ratio — K²/R² — decides which body reaches the bottom of a slope first.
Two circular-motion pages sit here too (34 questions together, 18% HARD each): the kinematics of angular speed and the dynamics of banking, the conical pendulum and the vertical circle. They share one idea with Laws of Motion — a free-body diagram with the centripetal force as the net inward force.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
Conservation of angular momentum
I₁ω₁ = I₂ω₂ when no external torque acts. Kinetic energy is NOT conserved when a body changes shape.
Rolling without slipping
Total KE = ½mv²(1 + K²/R²). Down a slope, the body with the smallest K²/R² arrives first: sphere (2/5), then disc (1/2), then ring (1).
Moment of inertia and radius of gyration
Learn the standard list — ring MR², disc ½MR², solid sphere ⅖MR², rod about centre ML²/12 — and I = MK².
Axis theorems
Parallel: I = I_cm + Md². Perpendicular (flat bodies only): I_z = I_x + I_y. The HARD questions stack two shifts or combine several bodies.
Circular motion dynamics
Banking: tan θ = v²/rg. Vertical circle: the minimum speed at the top is √(gr), at the bottom √(5gr).
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Using the perpendicular-axis theorem on a 3-D body
I_z = I_x + I_y holds only for flat (planar) bodies. Applied to a sphere or a cylinder it gives a plausible, wrong option.
Conserving energy when a body changes shape
When a skater pulls in her arms, Iω is conserved and the kinetic energy RISES (she does work). Keeping KE constant instead gives a wrong ω.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Rotational Dynamics notesDrill every rotational dynamics question
128 questions from the bank, scoped to 6 bundled subtopics.
Drill one subtopic at a time
The 6 subtopics this playbook covers, in catalog order.
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