Question

Find the dimensions of
(a) angular speed $\omega$
(b) angular acceleration $\alpha$,
(c) torque $\Gamma$ and
(d) moment of inertia $I$

Answer 1

part- (a)
Angular speed $\omega =\frac{V}{r}$
Dimension of angular speed $=\frac{dimensionofV}{dimensionofr}$ $=\frac{\left[L{T}^{-1}\right]}{\left[L\right]}$
$=\left[T^{-1}\right]$
part-(b)
Angular acceleration $\alpha =\frac{\omega }{t}$
Dimension of angular acceleration $=\frac{dimensionof\omega }{dimensionoft}$ $=\frac{\left[T^{-1}\right]}{\left[T\right]}$
$=\left[T^{-2}\right]$
part-(c)
torque $\Gamma =F.r$
Dimension of $\Gamma =dimensionofF\times dimensionofr$
$=\left[ML{T}^{-2}\right]\times \left[L\right]$
$=\left[M{L}^2{T}^{-2}\right]$
part-(d)
moment of inertia $I=m.r^2$
Dimension of $I=\left[M\right]\times \left[L^2\right]$
$=\left[ML^2\right]