Question 101: Units , Dimensions and Error Analysis

Question

The dimensional formula of angular impulse is :

Accepted Answer

Angular impulse is given when a torque is applied for a certain amount of time. The angular impulse changes the angular momentum of an object and has the same dimensions as angular momentum.
The dimensional formula for torque $	au$ is the same as that for work, since torque is a kind of rotational work, which is given by force times distance (or in rotational terms, it can be considered as force times lever arm). The dimensional formula for force is $\left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}ight]$, and when multiplied by distance $\left[\mathrm{L}ight]$, we get:
$\left[\mathrm{Torque}ight] = \left[\mathrm{M} \mathrm{L} \mathrm{T}^{-2}ight] 	imes \left[\mathrm{L}ight] = \left[\mathrm{M} \mathrm{L}^2 \mathrm{T}^{-2}ight]$
Now, angular impulse is torque times time, so we multiply the dimension of torque by time $\left[\mathrm{T}ight]$:
$\left[\mathrm{Angular\ Impulse}ight] = \left[\mathrm {M} \mathrm{L}^2 \mathrm{T}^{-2}ight] 	imes \left[\mathrm{T}ight] = \left[\mathrm{M} \mathrm{L}^2 \mathrm{T}^{-1}ight]$
So the correct dimensional formula for angular impulse is given by Option C, which is $\left[\mathrm{M} \mathrm{L}^2 \mathrm{T}^{-1}ight]$.

Answer

$\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]$

Answer

$\left[\mathrm{M} \mathrm{L}^{-2} \mathrm{~T}^{-1}\right]$

Answer

$\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1}\right]$

Answer

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

Units , Dimensions and Error Analysis

The dimensional formula of angular impulse is :

Choose the correct answer: