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Introduction to Physics — Physics STD 12 Science — Question

Bihar BoardEnglish MediumSTD 12 SciencePhysicsIntroduction to Physics2 Marks
Question
Find the dimensions of:

  1. Angular speed $\omega.$
  2. Angular acceleration $\alpha.$
  3. Torque $\tau$ and
  4. 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

  1. Angular speed $\omega=\frac{\theta}{\text{t}}=[\text{M}^0\text{L}^0\text{T}^{-1}]$

  2. Angular acceleration $\alpha=\frac{\omega}{\text{t}}=\frac{\text{M}^0\text{L}^0\text{T}^{-1}}{\text{T}}=[\text{M}^0\text{L}^0\text{T}^{-2}]$

  3. Torque $\tau=\text{Fr}=[\text{MLT}^{-2}][\text{L] = [ML}^2\text{T}^{-2}]$

  4. Moment of inertia $=\text{Mr}^2=[\text{M}][\text{L}^2]=[\text{ML}^2\text{T}^0]$

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