Physics Rotational Motion Equations

ω = ω₀ + αt

Find final angular velocity when you know angular acceleration and time.

Δθ = ω₀t + ½αt²

Find angular displacement when you know initial angular velocity, angular acceleration, and time.

ωf² = ω₀² + 2αΔθ

Relate angular velocities, acceleration, and displacement without needing time.

v = 2πr/T

Find linear (tangential) speed from radius and period.

T² = (4π²/GM)R³

Kepler's 3rd Law: Relates orbital period and orbital radius for planets/satellites.

a = rα

Find tangential (linear) acceleration from radius and angular acceleration.

ac = v²/r

Find centripetal acceleration toward the center of a circular path.

s = rθ

Find arc length traveled based on radius and angle rotated (in radians).

v = rω

Relate linear speed to angular speed and radius.

T = 1/f

Relate period (seconds per cycle) to frequency (cycles per second).

vesc = √(2GM/r)

Find escape velocity needed to leave a planet's gravitational pull.

2π = 360° = 1 revolution

Conversion between radians, degrees, and revolutions.