Dimensional Formula of Impulse

An impulse is a huge force that acts in a short period with finite momentum. We see impulse in our day-to-day activities; when we break a wooden piece with an axe with so much force, it breaks immediately, right? This is a classic example of impulse. We can find impulse by using the formula, impulse = force * time. It is a product of force and time. The unit in which impulse is measured is Newton-second(N-s).

Dimensional analysis

Physical quantities are related to the dimensions of the measurement units used to define them. This helps us perform mathematical calculations that are easier, more precise, and quicker. In other words, it is the study of dimensional formulae. It is the technique used to manipulate dimensional formulae.

Before studying the dimensional formula, we should first understand dimensional constants:

The dimensional constants are the numbers that specify the dimensions of an object. In other words, they describe the shape and size of an object. The dimensional constants are written as a series of numbers separated by commas, each number representing a value followed by a unit of measurement: D=1, m = metre, in = inch, ft = foot, yd = yard, km=kilometre, and so on. The first dimension constant, D, is used to specify the size of an object in terms of length.

Dimensions in units and measurements

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. 

An example of writing dimensions

Let’s take the formula of the area of the rectangle

Area of the rectangle = length x breadth

= [x ]    ( where breadth is also showing the length of the side)

= [L1] X [L1]

= [L2]

Here, we can see the length 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]

Impulse equation

Impulse can be defined as the product of the net force that acts on an object for a certain period. In mathematical terms, the equation of impulse (assuming that force is constant) can be written as: 

J = F ⋅t

where J is the impulse;

F is the force;

and, t is the time for which force is applied

Here ‘J’ is directly proportional to the time ‘t’.

Impulse can also be defined as the change in momentum and can be equated as;

J = m × v,

where m is the mass of the body

and v is the velocity of the body by which the body is moving.

Hence, velocity can be articulated as 

v = vf – vi

where;

vf is the final velocity and 

vi is the initial velocity

Therefore, the impulse force is written as,

f = m(vf – vi) / t

Impulse is expressed in kg m s-1 and the impulsive force is expressed in Newton (N).

Dimensional formula of impulse

We know that the formula of impulse is j = force * time

j = F*t

The dimensional formula of force is given by [M1L1T-2]

The dimensional formula of time is given by [M0L0T1]

j = [M1L1T-2] * [M0L0T1]

  = [M1L1T-1]

Therefore the dimensional formula of impulse is given by  [M1L1T-1]

Dimensional formula of impulse importance

• The dimensional formula of impulse helps us understand the physical correctness of any equation involving force.
• It helps us understand the relationship between different physical quantities involving impulse.
• It helps us in converting units from one physical quantity to another.
• In any relationship, the constant dimensions can be found using this analysis.

The formula of impulse importance

Impulse plays a vital role in our life. In sports activities, especially sports-related to throwing, the impulse is necessary. Airbags in our cars are designed taking into account the impulse we are going to experience. To calculate impulse in all such instances, the formula of impulse is required.

Real-life applications of impulse

Some real-life applications in which we can see impulse are listed below:

• Hitting a golf ball
• Tossing a coin
• Airbags deployed in the car
• Hitting the ball with a bat in the cricket match
• Kickstarting a motorbike

Conclusion

This article briefly acts as the formula of impulse notes for UPSC, and it explains what is impulse, its definition, formula, and importance. Impulse can be defined as a term in physics that is proportional to the force. It is represented by ‘J’ and is expressed in Newton-seconds. It is often referred to as the fast-acting force that acts for a short time interval.