Question

The dimension for angular velocity is:
1. T^-2
2. L³T
3. LT³
4. T^-1

Answer 1

Correct Answer - Option 4 : T^-1

Explanation: 

Angular velocity: Angular velocity is a vector quantity and is described as the rate of change of angular displacement which specifies the angular speed or rotational speed of an object and the axis about which the object is rotating. The amount of change of angular displacement of the particle at a given period of time is called angular velocity. 

ω = dθ / dt  Where, dθ, is the change in angular displacement dt, is the change in time t. 

Dimension:

Angular velocity = Angular displacement × [Time]^-1........(1)

The dimensional formula of Angular displacement = [M⁰L⁰T⁰]..........(2)

And, dimension of time = [M0L0T¹]..........(3)

On substituting equation (2) and (3) in equation (1) we get,

Angular Velocity = Angular displacement × [Time]-1

or, ω = [M0L0T0] ×  [M0L0T1]^-1 = [M0L0T^-1]