# Find the Dimensions of Angular Speed ω. - Physics

Sum

Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque τ and
(d) moment of interia I.
Some of the equations involving these quantities are $\omega = \frac{\theta_2 - \theta_1}{t_2 - t_1}, \alpha = \frac{\omega_2 - \omega_1}{t_2 - t_1}, \tau = F . r \text{ and }I = m r^2$.
The symbols have standard meanings.

#### Solution

(a) Dimensions of angular speed,
$\omega = \frac{\theta}{t} = \left[ M^0 L^0 T^{- 1} \right]$
(b) Angular acceleration,
$\alpha = \frac{\omega}{t}$
Here, ω = [M0L0T−1] and = [T]
So, dimensions of angular acceleration = [M0L0T−2]
(c) Torque, τ =Frsinθ
Here, F = [MLT−2] and r = [L]
So, dimensions of torque = [ML2T−2]
(d) Moment of inertia = mr2
Here, m = [M] and r2 = [L2]
So, dimensions of moment of inertia = [ML2T0]

Concept: What is Physics?
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 1 Introduction to Physics
Exercise | Q 2 | Page 9
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