Find the dimensions of : 1. Angular speed . 2. Angular acceleration . 3. Torque and 4. Moment of interia I. Some of the equations involving these quantities are = _2- _1 t_2-t_1 , = _2- _1 t_2-t_1 , =F.r and I = mr^2. The symbols have standard meanings.

1. Angular speed = t =[M^0L^0T^ -1 ] 2. Angular acceleration = t = M^0L^0T^ -1 T =[M^0L^0T^ -2 ] 3. Torque =Fr=[MLT^ -2 ][L] = [ML^2T^ -2 ] 4. Moment of inertia =Mr^2=[M][L^2]=[ML^2T^0]

Find the dimensions of : 1. Angular speed . 2. Angular accelerati…

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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.

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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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