Force is one of the most fundamental components that exists in our universe. Force is everywhere, in between the celestial bodies, like stars and planets, and in between the very small subatomic particles like electrons, protons, etc. Newton is the unit of Force. Newton’s 2nd law can be defined as an external influence that changes or attempts to change the motion of a body. Although force can be classified into various subclasses on the basis of its type and strength, conceptually, it can be imagined as either pull or push type in nature. Various forces exist in nature, for example, gravitational force, magnetic force, nuclear force, etc. In these notes of the dimensional formula of Newton, we will learn how to deduce the dimensional formula of force, meaning of momentum, and other related questions.
Force is defined as the push or pull an object exerts on another. When two items come into contact with each other, they both exert a force on each other. Stretch and squeeze are other words that can be used to describe force. What does it mean to have “force” in physics?
“Push or pull that alters the velocity at which anything with mass travels.”
You can find out how much force is at work by utilising a spring balance. Newton (N) is the SI unit of force.
The dimensional analysis uses a set of units to determine the form of an equation, or more commonly, to ensure that the result of a computation is correct as a safeguard against many common errors.
The dimensions can be written as the powers of the fundamental units of length, mass, and time. It depicts their nature and does not show their magnitude.
Let’s take the formula of the area of a rectangle.
Area of the rectangle = length x breadth
= [L1] X [L1] (where breadth is also showing the length of the side)
= [L2]
Here, we can see length raised to the power of 2 and we cannot find the dimension of mass and time.
Hence, the dimension of the area of a rectangle is written as [M0 L2 T0]
The dimensional formula depicts the dependency of a physical quantity with fundamental physical quantity, along with the powers.
Let’s take the formula of speed
Speed = Distance / Time
The distance can be written in length [L]
Time can be written as [T]
The dimensional formula would be [ M0 L1 T-1]
Hence, we can conclude that speed is only dependent on length and time, not on mass.
As mentioned above, it is a unit of force and force can be defined as the product of mass and acceleration.
So, F(N) = mass x acceleration
Dimension of newton = Dimension of mass x Dimension of acceleration
Dimension of mass = [M]
Dimension of acceleration (It is the rate of change of velocity with time)
= [velocity]/[time]
= [displacement]/[time×time]
= L/T×T
= LT-2
So, the dimension of Newton = [MLT-2]
Now, we can say that the dimensional formula of newton is [MLT-2]
The meaning of momentum can be described in various ways, but in simple words, it gives the idea of motion of a body. It is defined as the product of mass and the velocity of the body. Momentum can be defined for both linear as well as circular motion. If a body is at rest, the momentum will be zero.
Momentum = mass × velocity
In these notes of the dimensional formula of Newton, we learnt the derivation of the dimensional formula of Newton and the meaning of momentum. With the help of the dimension of force, we can deduce dimensions of other quantities, such as momentum etc. Momentum is also a very useful concept having various implementations. For example, using the conservation of linear momentum law we can find the velocity of a body, given the other required quantities are known.
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