Question

what is dimensional formula of Angular velocity?????​

Answer 1

Answer:

Explanation:

The dimensional formula of angular velocity is given by,

[M0 L0 T-1]

Where,

M = Mass

L = Length

T = Time

Derivation

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

The dimensional formula of Angular displacement = [M0 L0 T0] . . . . (2)

And, the dimensions of time = [M0 L0 T1] . . . (3)

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

Angular Velocity = Angular displacement × [Time]-1

Or, v = [M0 L0 T0] × [M0 L0 T1]-1 = [M0 L0 T-1]

Therefore, the angular velocity is dimensionally represented as [M0 L0 T-1].

Answer 2

Solution:

We know that,

$\boxed{\sf{\blue{Angular\:velocity\:=\:\dfrac{Angular\:displacement}{Time}}}}$

[ω] = $\dfrac{\theta}{t}$........(1)

Let's find dimensional formula of angular displacement first.

Angular displacement = $\sf{\dfrac{Arc\:length}{Radius}}$

$\longrightarrow$ [ $\theta$ ] = $\dfrac{[L]}{[L]}$

$\longrightarrow$ [ $\theta$ ] = [M⁰L⁰T⁰]

Hence, dimensional formula of Angular displacement is [M⁰L⁰T⁰]

Also, we need the dimensional formula of time to get dimensional formula of Angular speed.

Substitute the dimensional formulas of Angular displacement and time in eq (1).

$\longrightarrow$ [ω] = $\sf{\dfrac{M^{0} L^{0} T^{0}}{T}}$

$\longrightarrow$ [ω] = [M⁰L⁰T-¹]

Hence, dimensional formula of Angular speed will be [M⁰L⁰T-¹].