Angular Acceleration Explained

Definition: Angular acceleration (α) is the rate of change of angular velocity (ω) over time.
Formula: α = (ω_f - ω_i)/t
Unit: radians/second² written as rad/s²

Quantities are classified as belonging to two distinct worlds; namely, the scalar and the vector. Scalar quantities have only the magnitude while vector quantities have both magnitude and direction of motion.

Every scalar quantity is associated with an analogous vector quantity. Linear velocity and acceleration from the scalar group are analogous to angular velocity and angular acceleration respectively. Acceleration is important in kinematics.

All three kinematical equations involve this quantity. Newton's second law that talks about the force acting on a body, would have no meaning without acceleration. The law says that the force acting on a body is equal to the product of its mass and acceleration.

Bodies that move along a circular path have angular acceleration. Owing to the circular path of motion, their direction of motion does not remain constant. The bodies that move in a straight line possess linear velocity while the ones moving in a circular manner possess angular velocity. Angular velocity changes with time, giving rise to the concept of angular acceleration.

Angular acceleration is the rate of change of angular velocity with respect to time. It is a vector quantity as it involves both magnitude and direction. We can say that angular acceleration = (final angular velocity - initial angular velocity)/time.

It is the deviation in angular velocity over time, and is denoted by omega (ω). It is the time derivative of angular velocity.

What is angular velocity? It is the time derivative of angular distance, with its direction perpendicular to the plane of angular motion. In short, angular velocity is the rate of change of angular distance with respect to time and angular acceleration is the rate of change of angular velocity over time.

The SI unit of angular acceleration is radians per second squared and is denoted by the symbol alpha (α). While discussing angular acceleration, we consider circular motion and this is the reason why the unit radian comes into picture.

Radians correspond to the scalar quantity 'degree' that is used to measure angles. Consider a circle with two radii that make it look like having cut a piece of pie. The angle between the two radii, if measured in radians, is the division of the length of the arc formed by the two radii by the length of the radius.

The SI unit for angular acceleration is derived from this unit of angular measurement.

The angular acceleration vector does not always point in the direction of the angular velocity vector. Imagine a car speeding along a road. While the car's velocity is directed forward, its angular acceleration vectors point along the direction of the axles of the car wheels.

In case there is a clockwise increase in the angular velocity, the angular acceleration vector points away from the observer, while in case of a counter-clockwise increase in angular velocity, the acceleration vector points towards the observer.

We all know that the force acting on an object is the product of its mass and acceleration. On similar lines, Newton's second law can be adapted to rotational motion by replacing force with torque, mass with moment of inertia, and linear acceleration with angular acceleration.

For all constant values of torque, the angular acceleration also remains constant, while the angular acceleration changes with time in case of a non-constant torque.

What's interesting about kinematics is that it tries to measure all forces in nature by taking into account two basic quantities; the mass that is characteristic to every concrete body and a change in its velocity represented by acceleration.