What is the Dimension of Momentum

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Dimensional Formula of Momentum

with its Derivation

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In this article, we will find the dimension of Momentum

Dimensional formula for Momentum is

$[M^1L^2T^{-1}]$

Where
M -> Mass

L -> Length

T -> Time
We would now derive this dimensional formula.

Derivation for expression of Dimension of Momentum

Momentum is defined as the product for mass  and Velocity
$p= mv$
Where
m -> mass
v-> Velocity
p->Momentum

So,
Now the dimension of Mass= $[M^1]$
Lets derive the dimension of Velocity
$v= \frac {dx}{dt}$
or
$v = \frac {d}{t}$
Now
Where
d-> displacement
t -> Time

Now Dimension of Displacement = $[L^1]$

Hence dimension of Velocity= $\frac {[L^1]}{[T^1]}=[M^0 L^1T^{-1}]$

So, Dimension of Momentum is given by

$\text {Dimension of Momentum} =[M^1] \times [M^0 L^1T^{-1}] = [M^1L^1T^{-1}]$

Unit of Momentum is Kg m/s and it is denoted by letter $p$

Try the free Quiz given below to check your knowledge of Dimension Analysis:-

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