Question

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.

Answer 1

(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 = [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]