This HL-only mini-lesson covers Theme A.4 — Rigid body mechanics: torque and rotational equilibrium, moment of inertia, angular kinematics and dynamics (τ = Iα), angular momentum and rotational kinetic energy.
Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.
A.4 · torque
Torque and rotational equilibrium
Torque (moment) is the turning effect of a force about a pivot. It is largest when the force is perpendicular to the position vector:
τ = Fr sinθtorque (N m) = force × distance from pivot × sin(angle between them)
A rigid body is in equilibrium only if BOTH the resultant force is zero (no linear acceleration) AND the resultant torque is zero (no angular acceleration).
Quick check
Quick check
?A spanner is used to loosen a bolt. To get the maximum turning effect for a given force, you should push:
Calculate
Calculate
#A force of 20 N acts at right angles to a spanner, 0.30 m from the pivot. Find the torque.
Rotation mirrors linear motion. Angular displacement θ, angular velocity ω and angular acceleration α obey suvat-style equations for constant α (e.g. ω = ω₀ + αt). The rotational Newton's second law uses the moment of inertia I:
τ = IαI plays the role of mass for rotation; it depends on how mass is distributed
Worked example — a spinning disc
A disc starts from rest (ω₀ = 0) with angular acceleration α = 3.0 rad s⁻² for 4.0 s.
ω = ω₀ + αt = 0 + 3.0 × 4.0 = 12 rad s⁻¹
Calculate
Calculate
#A wheel starts from rest and has angular acceleration 3.0 rad s⁻² for 4.0 s. Find its final angular velocity.
rad s⁻¹
Hint: ω = ω₀ + αt = 0 + 3.0 × 4.0.
Calculate
Calculate
#A resultant torque of 8.0 N m acts on a body of moment of inertia 2.0 kg m². Find its angular acceleration.
rad s⁻²
Hint: τ = Iα → α = τ ÷ I = 8.0 ÷ 2.0.
A.4 · energy & momentum
Rotational energy & angular momentum
A rotating body stores rotational kinetic energy and carries angular momentum:
E_K = ½Iω² · L = Iωangular momentum L is conserved if the resultant external torque is zero
A spinning skater who pulls their arms in reduces I, so ω rises to keep L = Iω constant — a direct demonstration of angular-momentum conservation.
Calculate
Calculate
#A flywheel of moment of inertia 0.50 kg m² spins at 10 rad s⁻¹. Find its rotational kinetic energy.
J
Hint: E_K = ½Iω² = ½ × 0.50 × 10².
Calculate
Calculate
#A body of moment of inertia 0.20 kg m² rotates at 15 rad s⁻¹. Find its angular momentum.
kg m² s⁻¹
Hint: L = Iω = 0.20 × 15.
Quick check
Quick check
?An ice skater spinning with arms outstretched pulls their arms inwards. Ignoring friction, what happens?
Sort it
Sort each rotational statement
Tap an item, then tap the group it belongs to.
🌀 Angular kinematics
⚙️ Rotational dynamics
🔁 Energy / momentum
Match it
Match the linear quantity to its rotational analogue
Tap a statement on the left, then its match on the right.
Statement
Answer
Recap
The big ideas to know
Torque: τ = Fr sinθ; maximum when force ⟂ to the arm
Equilibrium: resultant force AND resultant torque both zero
Dynamics: τ = Iα; I is the rotational analogue of mass
Kinematics: ω = ω₀ + αt and the other suvat analogues
Conservation: E_K = ½Iω²; L = Iω conserved with no external torque
That completes Rigid Body Mechanics for IB Diploma Physics HL. Press Finish to see your score.
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