This article will look at the dimensions of impulse and momentum and check whether the two dimensions are the same.
For instance, a question was asked in this line in a particular exam. The question says the dimensional formula for impulse is the same as (a) Momentum (b) force (c) rate of change of momentum (d) torque
Dimensional analysis is the study of the relation between physical quantities based on their units and dimensions. It is used to convert a unit from one form to another. Also, it will be easy to know the S.I. base unit of any quantity in physics.
To find the dimension of any quantity, we make use of length, mass, and time. The symbols that are used to specify length, mass, and time are [L], [M], [T], respectively. They are usually enclosed in brackets.
Impulse
The first thing to do is to write the formula for impulse. Impulse is expressed as force x time
Mathematically,
Impulse = force (F) x time (T)
The next thing is to find the dimension of force and that of time
Force = mass x acceleration = MLT-2
Time = T
So, impulse = MLT-2 x T = MLT-1
Therefore, the dimension of impulse is MLT-1
Momentum
Like I did for impulse, I will first write the formula for momentum. Momentum is mass x change in velocity
Momentum = mass x velocity
Mass = M
Velocity = LT-1
Momentum = M x LT-1 = MLT-1
Therefore, the dimension of momentum is MLT-1
Read: Dimension of pressure, power, force, energy
Impulse and momentum have the same dimension from what I have explained above. To also validate our result, let’s check Newton’s second law of motion
It states that the rate of change in the momentum of an object is proportional to the force applied and takes place in the direction of the force.
Mathematically, Force = m(v-u) /t
If cross multiply,
F *t = M(V-U)
So, this shows that impulse is equal to momentum.
