**impulse dimensional formula:** In physics, the term “impulse” is used to describe or measure the effect of a force working over time to modify an object’s momentum. It is denoted by the letter J and is usually measured in Newton seconds or kilogrammes per second.

**WHAT IS THE DIMENSIONAL FORMULA FOR IMPULSE?**

The dimensional formula of impulse is given by,

M1 L1 T-1

Where,

M = Mass

L = Length

T = Time

**Derivation**

Impulse (I) = Force × Time . . . . (1)

Since, Force (F) = Mass × Acceleration = M × [LT-2]

∴ The dimensional formula of force = M1 L1 T-2 . . . . (2)

On substituting equation (2) in equation (1) we get,

Impulse = Force × Time

Or, I = [M1 L1 T-2] × [T] = [M1 L1 T-1].

Therefore, the impulse is dimensionally represented as [M1 L1 T-1].

**understanding impulse and momentum**

Momentum is a term that we frequently hear in ordinary conversation. Sports teams and political candidates are sometimes informed that they have “a lot of momentum.” In this case, the speaker usually indicates that the team or candidate has had a lot of recent success and that changing their trajectory would be tough for an opponent. This is also the essence of meaning in physics, however, we must be much more exact in physics.

Momentum is a measure of mass in motion: how much mass is moving and how fast. It is commonly denoted by the letter p.

So, P = m.v

The mass is m, and the velocity is v. Momentum is measured in kilogrammes per second, and it is always a vector quantity. Because of this straightforward equation, doubling an object’s mass or velocity will simply double its momentum.

The link between momentum and force is quite beneficial. Change in velocity Δv can alternatively be expressed as a⋅Δt, as you may recall from the kinematic equations.

As a result, any change in momentum as a result of acceleration can be expressed as:

Δ**p**=*m*⋅Δ*v*

=*m*⋅**a**⋅Δ*t*

=**F**⋅Δ*t*

When a net force is applied to a body, it creates an acceleration, which modifies the velocity of the body. A bigger net force causes more acceleration than a smaller net force. The overall change in motion of the item may be the same if the large and small forces occur at separate times. The combination of force and time in which it acts is a valuable quantity that defines impulse.

The impulse is defined as the product of the average net force acting on an object during a given period.

The following is the impulse equation:

J = F⋅Δt

It’s worth noting that we assume force remains constant over time.

Like force, an impulse is a vector quantity with a direction.

**WHAT IS IMPULSE-MOMENTUM THEOREM**

Collisions are governed by the rules of momentum and the first law (also known as the change in impulse equation). A collision occurs when a body is subjected to a force over a period of time, causing a change in momentum. As a result of a force occurring for a specific amount of time, the body either slows down, speeds up, or changes direction.

When an item collides, it receives an impulse that corresponds to a change in momentum. Consider a sprinting football player colliding with a defensive back on the field. As a result of the contact, the halfback’s speed and momentum alter.

The Impulse-Momentum theorem aids in the understanding of the two concepts. The theorem states that the change in an object’s momentum is proportional to the amount of impulse applied to it.

In general, students should know that impulse is a measurement of how much momentum varies. We also get an alternative formula here, which is as follows:

Where,

p_{1 }= initial momentum

p_{2 }= final momentum

**examples of impulse**

The following are a few examples of impulse:

When someone falls from a bed to the floor, they suffer greater damage than if they fall into a sand pile. Because the sand yields more than the cemented floor, the contact time increases and the force impact decreases.

Nylon ropes are also used in the sport of rock climbing for the same reason. Climbers attach themselves to the rock faces with nylon ropes. If a rock climber loses her grip on the rock, she will begin to tumble. In this situation, the rope will ultimately slow her down, preventing her from falling to the ground below.

In racket and bat sports, hitters are typically trained to follow through when striking a ball. The act of following through on a collision between bats/rackets and balls has been shown in high-speed footage to increase the duration of the impact. This increase in time must result in a change in another variable, according to the impulse-momentum change theorem.