Rotational Motion
12 topics · 12 interactive simulations
Angular Kinematics
ω = ω₀ + αt, θ = ω₀t + ½αt² — see disk spin with live ω(t) and θ(t) plots.
Moment of Inertia
I formulas for 6 common shapes — solid/hollow sphere, cylinder, rod.
Torque
τ = r × F = rF sinθ — drag angle and watch rotation direction flip.
Parallel Axis Theorem
I = I_cm + Md² — shift the axis and see I grow quadratically with d.
Rotational Kinetic Energy
KE_rot = ½Iω² — compare with translational KE for rolling objects.
Conservation of Angular Momentum
L = Iω conserved — pull string shorter, ω grows as (r₀/r)².
Rolling Motion
a = g sinθ/(1 + k²) — 4 shapes race down an incline; sphere wins.
Linear ↔ Angular Variables
v = ωr, a_t = αr, a_c = ω²r — drag a particle on a rotating disc to see all three.
Lever Balance (Torque)
Two masses on a beam — adjust weights and arms; see torque balance live.
Radius of Gyration
k = √(I/M) — see equivalent ring radius for ring, disc, rod, sphere, shell.
Rolling With Slipping
Independent v and ω — detect skidding (v > ωR) vs spinning (ωR > v) vs pure rolling.
Gyroscopic Precession
Spinning top — see L precess about vertical at Ω = mgr/(Iω). Real animatronic feel.