Question

Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque $\tau$ and
(d) moment of interia I.
Some of the equations involving these quantities are
$\omega =\frac{{\theta }_2-{\theta }_1}{t_2-t_1},\alpha =\frac{{\omega }_2-{\omega }_1}{t_2-t_1},\tau =F.r\mathrm{and}I=m{r}^2$.
The symbols have standard meanings.

Answer 1

(a) Dimensions of angular speed, $\mathrm{\omega }=\frac{\mathrm{\theta }}{t}=\left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^{-1}\right]$

(b) Angular acceleration, $\mathrm{\alpha }=\frac{\mathrm{\omega }}{t}$
Here, ω = [M⁰L⁰T⁻¹] and t = [T]
So, dimensions of angular acceleration = [M⁰L⁰T⁻²]

(c) Torque, τ =Frsin$\theta$
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]