Question

What is angular acceleration? How is it related to linear acceleration?

Answer 1

Hint It is the basic definition of physics. Without knowing this we cannot handle any of the questions of physics. Angular acceleration deals with circular motion whereas, linear acceleration deals with linear motion of an object. These are very basic definitions. There is a relation between the angular acceleration and linear acceleration also.

Complete answer:
Angular acceleration is defined as the rate time rate of change of angular velocity. It is of two types: spin angular acceleration and orbital angular acceleration. Its unit is $\dfrac {rad} {{{s} ^ {2}}} $ and is donated by $\alpha $. Spin angular acceleration is defined as angular acceleration of a rigid body with respect to its centre of rotation whereas; orbital angular acceleration is defined as the angular acceleration of a point particle with respect to a fixed origin. The expression for angular expression is given by –
$\alpha =\Delta \omega \Delta t$ where, $\Delta \omega $ = change in angular velocity,
$\Delta t$ = change in time.
Linear acceleration is defined as the uniform acceleration of an object with increasing and decreasing velocity. The acceleration depending upon velocity can decrease or increase. The relation between linear acceleration and angular acceleration is that both are directly proportional to each other. So, we can write its expression as –
$a=\alpha r$ where, r = radius of circular path.

Note:
From the above expressions we can say that if angular acceleration increases the, linear acceleration also increases also, when angular acceleration decreases then, linear acceleration decreases. Angular acceleration is just a number when written in 2-D with a negative or a positive sign. This sign is decided by the change in the angular speed.