Rotational Motion Formulas
A complete list of rotational motion formulas, covering torque, moment of inertia, angular velocity and acceleration, and rotational kinetic energy.
12 formulas. Use the interactive searcher to solve for any variable and convert units.
Open the interactive searcher →Torque
τ = r·F·sinθ
τ torqueN·mr radiusmF forceNθ anglerad
Angular velocity
ω = θ / t
ω angular velocityrad/sθ angleradt times
Rotational KE
KE = ½·I·ω²
KE kinetic energyJI moment of inertiakg·m²ω angular velocityrad/s
Angular acceleration
α = Δω / Δt
α angular accelerationrad/s²Δω change in angular velocityrad/sΔt times
Rotational Newton's 2nd law
τ = I·α
τ torqueN·mI moment of inertiakg·m²α angular accelerationrad/s²
Moment of inertia (point)
I = m·r²
I moment of inertiakg·m²m masskgr radiusm
Moment of inertia (disk)
I = ½·m·r²
I moment of inertiakg·m²m masskgr radiusm
Moment of inertia (rod, center)
I = (1/12)·m·L²
I moment of inertiakg·m²m masskgL lengthm
Tangential velocity
v = r·ω
v velocitym/sr radiusmω angular velocityrad/s
Tangential acceleration
a_t = r·α
a_t tangential accelerationm/s²r radiusmα angular accelerationrad/s²
Angular displacement
θ = ω₀·t + ½·α·t²
θ angular displacementradω₀ initial angular velocityrad/sα angular accelerationrad/s²t times
Rolling kinetic energy
KE = ½·m·v² + ½·I·ω²
KE kinetic energyJm masskgv velocitym/sI moment of inertiakg·m²ω angular velocityrad/s