Revise: Rotational Motion

θ = s/r, always in radians.

s=6m, r=4m → θ=1.5 rad.

ω = Δθ/Δt, in rad/s.

10 rad in 4s → ω=2.5 rad/s.

α = Δω/Δt, in rad/s².

2→10 rad/s in 4s → α=2 rad/s².

ω=ω₀+αt; θ=ω₀t+½αt²; ω²=ω₀²+2αθ.

ω₀=5, α=3, t=4 → ω=17, θ=44.

v = rω — linear speed depends on radius.

r=0.5m, ω=8rad/s → v=4 m/s.

aₜ = rα — tangential accel changes speed, not direction.

r=0.3m, α=6rad/s² → aₜ=1.8 m/s².

a_c = v²/r = ω²r, always toward the center.

v=20m/s, r=50m → a_c=8 m/s².

T = 1/f; ω = 2πf.

f=5Hz → T=0.2s, ω≈31.42 rad/s.

A full circle is 2π radians (360°).

The rotational counterpart of linear displacement.

ω is the same for every point on a rigid rotating object.

Earth's rotation: ω≈7.27×10⁻⁵ rad/s everywhere.

Negative α means the rotation is decelerating.

A washing machine spinning up from rest.

Only valid for constant angular acceleration.

Directly mirror the linear suvat equations.

Points farther from the axis move faster (larger v), same ω.

The outer edge of a spinning record moves fastest.

Different from centripetal acceleration, which changes direction.

A car tire speeding up from a stop.

Exists even at constant speed, since direction is changing.

Requires a net inward force to sustain (Chapter 2).

Larger frequency means smaller period.

T=0.1s → f=10Hz.