# Momentum And Its Conservation Formula

## Momentum and its Conservation Formula

The great scientist Isaac Newton had a significant influence on physics, and in Newtonian mechanics, momentum is a vector quantity that is the product of an object’s mass and velocity. The standard unit for measuring momentum is a kilogram-meter per second (kg m/s or kg m s-1). A quantity with a magnitude but no specific direction is referred to as a scalar quantity, whereas a quantity with magnitude and a specific direction is referred to as a vector quantity.

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## Momentum

The definition of momentum is a succinct and precise “mass in motion”. All objects have mass, so if an object with a mass greater than zero moves, it has momentum. The amount of momentum an object has is primarily influenced by two factors,

How much is being moved?

How quickly is everything moving?

It is directly influenced by mass and velocity. According to an equation, an object’s momentum is determined by multiplying its mass by its velocity.

Momentum= mass × velocity

In physics, the letter p in lowercase represents the quantity momentum. As a result, the previous equation can be written as:

p = m × v

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### Direction of momentum

The “direction of momentum is same as the direction of velocity” axiom holds true despite the fact that the direction of momentum can be expressed in a variety of ways depending on the number of dimensions involved. The example below will help you better understand this concept.

Considering that momentum is inversely proportional to velocity, consider a 1,000 kg truck travelling northward at a speed of 20 m/s relative to the surface of a highway. If the truck is driven, its momentum will be zero because it will be relative to the body of the driver. Additionally, if a person is standing by the side of the road, the truck’s momentum toward that person is 20,000 kgm/s northward.

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### Types of momentum

Momentum can be categorised into the following main categories depending on the type of motion:

• Angular Motion

It is calculated by dividing the mass of a body by its angular velocity. A single body can therefore possess two different types of angular momentum. Planetary bodies, like the Earth, for instance, have two types of momentum: one determined by how the body moves in relation to the Sun, and the other determined by how quickly the body spins on its own axis.

• Linear Motion

It is also referred to as force and is the amount of mass attached to a body that moves in a straight line. An external object’s force alone has the power to alter the trajectory of an object with linear momentum. For instance, if a dog accidentally runs into you as you are moving forward, your trajectory will be altered, and you may fall, but you shouldn’t be seriously hurt because the dog had a similar momentum to yours. However, you will be lucky to survive if you are struck by a truck, which has a higher linear momentum due to its high weight. The reason for this is that the truck has more force than you do.

• Conceptual Propulsion

Regardless of the type of momentum, the common meaning and its precise meaning are largely consistent.

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### Conservation of momentum and its formula

The ratio of an object’s mass to its velocity yields its momentum. The fundamental law of physics states that for two moving objects, if neither is being affected by any external forces, their total momentum before and after their interaction or collision will be the same. This relationship is referred to as “the conservation of momentum.”

The phenomenon of collision and explosion can be explained using this fundamental tenet of physics. You can explain momentum conservation by,

P1 (before) + P2 (before) = P1 (after) + P2 (after)

This equation holds true for the object that collides.

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### Derivation of conservation of momentum

Total momentum before collision = m1u1 + m2u2

Total momentum after collision = m1v1 + m2v2

Acceleration of car (a) = (v2 – u2)/t

Also, as F = ma

F1 = Force exerted by truck on the car.

F1 = m2(v2 – u2)/t

Acceleration of truck = (v1 – u1)/t

F2 = m1(v1 -u1)/t and F1 = -F2

m2(v2 – u2)/t = -m1(v1 – u1)/t

m2v2 – m2u2 = m1v1 + m1u1

Or

m1u1 + m2u2 = m2v2 + m1v1

### Sample Problems

Q. Newton’s laws of motion are connected to the law of conservation of momentum. What is the law of motion of Newton’s?

A. The third law of motion, according to Newton, which states that every action has an equal and opposite reaction, is connected to the law of conservation of momentum. For instance, when someone punches a wall, injuries are unavoidable because both hands receive the same amount of force.

Q. What is the momentum of the Earth’s recoil if a player launches a ball upward with ten units of momentum from the ground? Why doesn’t the player feel that recoil?

A. The earth sways backwards by ten units of momentum. The Earth’s recoil velocity is too small to be felt because of its extremely very large mass. As a result, neither players nor people in general experience recoil.

Q. Give some examples and the conservation of momentum formula.

A. The conservation of momentum equation is:

Total momentum of bodies before and after a collision equals each other.

Phenomena that adhere to momentum conservation

bullet and gun system

Vehicle collisions

various air balloon systems

Q. Describe how the Gun-Bullet system operates using the idea of momentum conservation.

A. The momentum lost by the primary object is strictly equal to the momentum gained by the secondary object under the theory of conservation of momentum. In this scenario, if a gun fires a bullet forward while exerting force on it, the bullet will apply an equal force to the gun while travelling in the opposite direction, causing it to move backwards or recoil. Despite the fact that the size of the action and reaction forces are equal, the effect on the gun and consequently the bullet is not equal because the gun’s mass is much greater than the mass of the bullet.

Q. What does the momentum conservation law say?

A. According to the law of conservation of momentum, absent an external force, the combined momentum of two or more bodies acting upon one another in an isolated system remains constant. As a result, momentum cannot be gained or lost.

Q. What law of motion serves as the foundation for the law of conservation of momentum?

A. Newton’s third law of motion, which states that every force has an equal and opposite reciprocating force, is the foundation for the law of conservation of momentum.