Angular Acceleration Calculator
Angular acceleration measures how quickly an object's angular velocity changes over time. Defined as alpha = (omega_2 - omega_1) / t, it is the rotational analog of linear acceleration. This calculator also computes angular displacement, number of revolutions, and tangential linear acceleration at a given radius.
Angular acceleration (α) is measured in rad/s² and describes the rate of change of angular velocity. Just as linear kinematics has equations for constant acceleration, rotational kinematics has analogous equations: α = (ω₂ - ω₁)/t, θ = ω₁t + ½αt², and ω₂² = ω₁² + 2αθ.
The angular displacement θ gives the total angle swept by the rotating object. Dividing by 2π converts to revolutions, which is useful for applications like motors, wheels, and gears. For example, a motor that sweeps 62.8 radians has completed exactly 10 revolutions.
The tangential linear acceleration at a point on the rotating body is a = α × r, where r is the distance from the rotation axis. This connects rotational and linear motion: a point on the rim of a spinning wheel experiences both tangential acceleration (from changing speed) and centripetal acceleration (from changing direction). Angular acceleration is fundamental to the design of engines, turbines, gyroscopes, and any rotating machinery.