Find the dimensions of

(a) angular speed $ω$

(b) angular acceleration $α$

(c) torque $Γ$ and

(d) moment of interia I.

Some of the equations involving these quantities are

$ω = \frac{θ_{2} - θ_{1}}{t_{2} - t_{1}}$ ,

$α = \frac{ω_{2} - ω_{1}}{t_{2} - t_{1}}$

$Γ = F j$ and $I = m r^{2}$ .

The symbols have standard meanings.

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Solution

(a) Angular speed,

$¯ ω = \frac{ω}{i} = [M^{\circ} L^{\circ} T^{- 1}]$

(b) Angular accelatration,

$α = \frac{ω}{t} = \frac{M^{\circ} L^{\circ} T^{2}}{T}$

$= [M^{\circ} L^{\circ} T^{- 2}]$

(c) Torque, $τ = F r = [M L T^{- 2}]$

$[L] = [M L^{2} T^{- 2}]$

(d) Moment of inertia

$= M r^{2} = [M] [L^{2}]$

$= [M L^{2} T^{\circ}]$

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