← HL Deep Dives — Rigid Bodies & Relativity
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HL Deep Dives — Rigid Bodies & Relativity

Chapter 1 · Rigid-body rotational dynamics

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Angular kinematics
ω=ω0+αt,θ=ω0t+12αt2\omega = \omega_0 + \alpha t,\quad \theta = \omega_0 t + \tfrac{1}{2}\alpha t^2
Rotational analogues of suvat.
Angular ↔ linear
v=ωr,a=αr,s=θrv=\omega r,\quad a=\alpha r,\quad s=\theta r
θ\theta in radians; 2π2\pi rad = one revolution.
Torque
τ=Frsin⁡θ=Iα\tau = Fr\sin\theta = I\alpha
Rotational form of F=maF = ma; N m.
Moment of inertia
I=∑miri2I = \textstyle\sum m_i r_i^2
Resistance to angular acceleration; kg m².
Rotational Newton 2
τ=Iα\tau = I\alpha
Net torque produces angular acceleration.
Angular momentum
L=IωL = I\omega
kg m² s⁻¹. Conserved when net external torque = 0 (figure-skater effect).
Rotational KE
Ek=12Iω2E_k = \tfrac{1}{2}I\omega^2
Common traps
Using degrees where radians are required; forgetting that rolling combines translational + rotational KE.