Find the dimensions of: 1. Angular speed . 2. Angular acceleratio… - Vidyadip

Question

Find the dimensions of:

Angular speed $\omega.$
Angular acceleration $\alpha.$
Torque $\tau$ and
Moment of interia I.

Some of the equations involving these quantities are

$\omega=\frac{\theta_2-\theta_1}{\text{t}_2-\text{t}_1},\alpha=\frac{\omega_2-\omega_1}{\text{t}_2-\text{t}_1},\tau=\text{F.r}$ and $\text{I = mr}^2.$

The symbols have standard meanings.

✓

Answer

Angular speed $\omega=\frac{\theta}{\text{t}}=[\text{M}^0\text{L}^0\text{T}^{-1}]$
Angular acceleration $\alpha=\frac{\omega}{\text{t}}=\frac{\text{M}^0\text{L}^0\text{T}^{-1}}{\text{T}}=[\text{M}^0\text{L}^0\text{T}^{-2}]$
Torque $\tau=\text{Fr}=[\text{MLT}^{-2}][\text{L] = [ML}^2\text{T}^{-2}]$
Moment of inertia $=\text{Mr}^2=[\text{M}][\text{L}^2]=[\text{ML}^2\text{T}^0]$

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