Dimension of Linear Momentum

The powers to which the fundamental units that are the unrelated units of measurement are raised for a physical quantity so as to get one unit of that quantity is considered as dimensions of that physical quantity.

Dimensional Formula

Dimensional formulas are often defined as the expression that shows the powers to which the fundamental units are to be raised to get one unit of a derived quantity.

Suppose the unit of a derived quantity is represented by Q. Then, Q can be given as- MaLbTc 

Thus, Q= MaLbTc

Which represents the dimensional formula of a physical quantity and the exponents in this case (a,b,c) are the dimensions.

Linear Momentum

From the study of Momentum, we know that momentum is the mass of the body times the velocity.

So mathematically p= m x v

Change in the momentum of the body remains proportional to the net force and the time over which the net force acts.

Now, we will find out how momentum and net force are related.

While learning kinematic equations, you have learned that with constant acceleration, the change in velocity Δv can also be given as aΔt.

So, the change in momentum following an acceleration can be given as-

Δp= mΔv

Therefore, m(aΔt)= FnetΔt

From the above equation, by rearranging the equation to get value of Fnet

Given the mass and the net force is constant

Fnet= \[\frac{\Delta p}{\Delta t}\]

From this, we can conclude that change in momentum is equal to the net force over a period of time. 

Now, inertia of translational momentum is described as linear momentum. Linear momentum does not have a direction as it is a vector quantity. Also, it has to be noted that the body’s momentum is in the same direction as its vector of velocity.

The SI unit of linear momentum is given as Kg m/s.

Formula for Dimensions of Linear Momentum

Linear Momentum is given by -

Linear Momentum  = Mass∗Velocity

Dimensions of mass = M

Dimensions of velocity = \[\frac{Length}{Time}\]

    = L T⁻¹

Therefore, Dimensions of Linear Momentum is given by - [M1 L1 T-1]

Where,

• M = Mass

• L = Length

• T = Time

Solved Examples to Calculate Linear Momentum

1. Find the linear momentum of the body having mass 10 kg, moving with the speed of 40 m/s.

Solution: Given mass of the body m= 10 kg

Velocity of the body v= 4 m/s

Linear momentum is given by-

P = mv

So, Momentum p= 10 x 40

p= 400 kg m/s

2. The linear momentum of a body of mass 5 kg is 40 kg m/s. What is the velocity with which the object is moving?

Solution: Mass of the body is m= 5 kg

Given linear momentum of the body p = 40 kgm/s

Linear momentum is given as p= mv

Rearranging the equation, v = \[\frac{p}{m}\]

So, v = \[\frac{40}{5}\]

v = 8 m/s

Derivation of Dimension of Linear Momentum

Linear Momentum = Mass × Velocity . . . . . . (1)

The dimensional formula of,

Mass = [M1 L0 T0] . . . . (2)

Velocity = [M0 L1 T-1] . . . . (3)

Let us substitute equation (2) and (3) in equation (1). Hence, we get,

Linear Momentum = Mass × Velocity

Or, L = [M1 L0 T0] × [M0 L1 T-1] = [M1 L1 T-1].

Therefore, the dimensional formula for linear momentum can be given by [M1 L1 T-1].

Linear Momentum Dimension

Linear momentum is a quantity measured by multiplying the system’s mass with its velocity. We must know that a large and fast-moving object will have greater momentum than a small and slow-moving object. It is given as p = mv. This means that it is directly proportional to the mass and velocity of the object. When the mass or the velocity is greater of the object, then the momentum is great too. The linear momentum conservation is exhibited by any object in which the momentum amount does not change. This quantity is a vector quantity which has the same direction as the velocity of the object. Its SI unit is written as kg.m/s.

This quantity was quite important for the development of classical physics just like the concept of energy was. It was termed as ‘quantity of motion’ because of its importance. Newton gave the second law of motion based on the momentum. He stated that the total external force is equal to the change of momentum in the system which is divided by time over which the change occurs. To learn more about linear momentum, you can log in or sign up to Vedantu and start learning more about this topic. Vedantu provides all the study materials required for this topic and you can also ask the Vedantu experts if you have subject-related doubts. This is free of cost and you can simply start learning by logging in today.