Angular acceleration

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In circular motion, angular acceleration is the rate of change of angular velocity with respect to time. The S.I. unit of angular acceleration is rad/s2. The dimensional formula is [T_2]. In uniform circular motion the angular velocity is constant, with the result that the angular acceleration in such a motion is zero.

Terms used to describe circular motion

In every circular motion, the terms used to describe the nature of the motion are angular displacement, time, angular velocity and angular acceleration. Average angular velocity and average angular acceleration are denoted by the following mathematical expressions:

• Average angular velocity: ωavg=∆θ/∆t

• Average angular acceleration: αavg=∆ω/∆t

Relation between angular acceleration and tangential acceleration

The angular acceleration α and the tangential acceleration in circular motion are related by the following expression:

• atan = r α

Thus the tangential force can be expressed as the product of the mass and the tangential acceleration.

There may be several components of torque for a single object. The sum of all the torques gives rise to the moment of inertia, which is basically the product of mass, the square of the radius of rotation and the angular acceleration.

Analogy between translational and rotational motion

It is possible to draw an analogy between linear translational motion and circular motion. The relationship between torque and angular acceleration is analogous to Newton's Second Law of motion, which refers to the conservation of momentum in objects in linear motion.

If torque is taken to be analogous to force in linear motion, the moment of inertia analogous to mass and the angular acceleration analogous to linear acceleration, the relationship seems to obey a rule similar to the Second Law.