Generally, quantities are classified as scalar or vector. Scalar quantities are those quantities which have only magnitude while vector quantities are those which have both direction of motion and magnitude. Each and every scalar quantity is related to a corresponding vector quantity. Linear acceleration and velocity from the scalar class are related to angular acceleration and angular velocity respectively. As we have learnt during our Physics tuition classes, acceleration is essential in kinematics.
Bodies moving along a circular path portray angular acceleration. Due to the circular trail of movement, their motion direction doesn’t remain constant. Bodies moving in a straight line have linear velocity while those moving in a circular motion have angular velocity. The angular velocity varies with time, bringing about the angular acceleration concept.
Angular acceleration can be defined as the rate of angular velocity change with respect to time. The angular acceleration is a vector quantity, since it involves both direction and magnitude. It can be clearly stated, angular acceleration = (final – initial angular velocity) / time. In other words, it’s the angular velocity deviation over time. We can as well say that it’s the angular velocity time derivative. Angular velocity is denoted by Omega.
Angular velocity can be defined as the angular distance time derivative, with a perpendicular direction to the angular motion plane. Basically, angular velocity is simply, the rate of angular distance change with respect to time.
Angular acceleration is measured in radians per square second and is denoted by Alpha. The radian unit comes into picture when dealing with angular acceleration because circular motion is considered. Radians corresponds to the scalar quantity, degree, which is used in angle measurement. Take into account a circle with two radii which makes it appear like a piece of pie which has been cut. The angle between these two radii, when measured in radians, is basically the arc length formed by these two radii divided by the radius of the circle.
Angular acceleration vector doesn’t constantly point in the angular velocity vector direction. Picture a vehicle speeding along a street. When the vehicle’s velocity is directed forward, the angular acceleration vector is pointed to the vehicle’s wheels axles’ direction. In case the angular velocity increases in the clockwise direction, the angular acceleration vector is directed away from the viewer, and when it increases in the counter-clockwise direction, the acceleration vector is directed towards the viewer.
Newton’s 2nd law can be applied to rotational motion by changing linear acceleration to angular acceleration, force to torque, and mass to moment of inertia. The angular acceleration stays constant, for all the constant values of torque, and then changes with time when there is a non-constant torque.