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Rotational kinematics
Beginner
Constant-α equations mirror linear ones.
θ = ω₀t + ½αt²With constant α: ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ. They are used the same way as linear equations.
A wheel stops from 10 rad/s with α = −2: turns 25 rad.
Check signs of α and ω.
In more detail
Rotational kinematics uses the same equations as linear kinematics with angular quantities: ω = ω0 + αt, θ = ω0 t + ½αt², and ω² = ω0² + 2αθ, for constant angular acceleration.
Real-world uses
- Calculating how many turns a flywheel makes as it slows to rest.
- Estimating the time for a centrifuge to reach its operating speed.
- A spinning turntable that slows down from a fixed speed follows the same pattern as a moving car with constant deceleration.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Can I use these for any rotation?
Only for constant angular acceleration.
What is the angular analogue of mass?
The moment of inertia.
How do I know which equation to use?
Use the same approach as linear motion, substituting angle for displacement, angular velocity for velocity and angular acceleration for acceleration.
Related topics in Rotational Motion
Angular acceleration · Radians and degrees · Relation between linear and angular quantities · Torque · Lever arm and moment · Equilibrium of a rigid body