Question

The dimensions of the ratio of angular to linear momentum are:

Answer 1

Linear momentum, $P=mv$

$=\left[M\right]\left[M^o{L}^1{T}^{-1}\right]$

$P=\left[M^1{L}^1{T}^{-1}\right]$ ...(1)

Whereas, angular momentum,

$L=Iw$

$L=\left[M^1{L}^2{T}^{-1}\right]$ ...(2)

From (1) and (2)

$\frac{\left[L\right]}{\left[P\right]}=\frac{\left[M^1{L}^2{T}^{-1}\right]}{\left[M^1{L}^1{T}^{-1}\right]}$

$\frac{\left[L\right]}{\left[P\right]}=\left[L\right]$