Question

Write your question here (Keep it simple and clear to get the best answer)what is the dimensions of angular velocity

Answer 1

Answer:

The dimensions of angular velocity is $[T^{-1}]$

Explanation:

We know that linear velocity is equal to the rate of change of linear displacement.

Similarly, in rotational motion, the analogous term for linear velocity is angular velocity.

Angular velocity is defined as the rate of change of angular displacement.

The angular displacement is the measure of the angle rotated by an object about a fixed point or the axis of rotation.

Therefore, the unit of angular displacement is measured in radians. We know that, the radian is a dimensionless quantity. So, its dimension is $[M^0L^0T^0]$

Now, time is measured in seconds. So, dimension of time is $[M^0L^0T]$

Therefore, the dimensions of angular velocity is given as:

$Angular\ velocity =\frac{Angular\ displacement}{Time}\\\\Dimensions=\frac{[M^0L^0T^0]}{[M^0L^0T]}\\\\Dimensions =[T^{-1}]$

Therefore, the dimensions of angular velocity is $[T^{-1}]$