A particle moves in a circle of radius r. Having moved an arc length s, its angular position is θ relative to its original position, where. An angular displacement is a change in angular position: where Δθ is the angular displacement, θ 1 is the initial angular position and θ 2 is the final angular position.

-Angular velocity is the change in angular displacement per unit time. The symbol for angular velocity is ω and the units are typically rad s -1. Angular speed is the magnitude of angular velocity. -The instantaneous angular velocity is given by Using the formula for angular position and letting, we have also -Using the formula for angular position and letting we have also where v is the translational speed of the particle. -Angular velocity and frequency are related by

A changing angular velocity indicates the presence of an angular acceleration in rigid body, typically measured in rad s −2. The average angular acceleration over a time interval Δt is given by

The instantaneous acceleration α(t) is given by Thus, the angular acceleration is the rate of change of the angular velocity, just as acceleration is the rate of change of velocity. The translational acceleration of a point on the object rotating is given by The radial acceleration (perpendicular to direction of motion) is given by.

I = mr 2.

Torque τ is the twisting effect of a force F applied to a rotating object which is at position r from its axis of rotation. Mathematically,

where r is the particle's position from the origin, p = mv is its linear momentum, and × denotes the cross product.