# Momentum Formula

The concept of Momentum in physics is very important without which most of the theories in physics will fail. The momentum can be calculated by multiplying the mass of the substance and its velocity. In physics, the momentum is of different types and different forms. Let’s know more about momentum and its formula.

Rene Descartes formulated momentum. When Rene Descartes was residing in Holland, he wanted to scientifically define how objects move. Rene began by assuming that the universe’s velocity was a conserved attribute and also put his theory to the test using collisions.

### Momentum

It is clear from the definition of momentum that an item has a significant momentum if its mass and velocity are both large. In calculating an object’s momentum, both factors are equally important. Consider a truck and a bicycle both speeding down the street. The truck has a significantly higher momentum due to its significantly bigger mass. However, if the truck were to stop, the least big bicycle would have the most momentum. Any item that is at rest has no momentum.

The momentum is the product of the mass of the particle and its velocity. It is denoted by (p).

p = mvIt is a vector quantity i.e. it has magnitude and direction.

**Types of momentum **

**Linear Momentum:**It is momentum in a particular direction.

**Angular Momentum:**Its momentum is inclined at some angle or has a circular path.

### Examples of momentum

- A car is moving at the speed of 40 km/hr, so here the car will have a certain mass, and the product of the mass and its velocity will give the value of the momentum.
- The swing at the playground has certain momentum and it is called angular momentum.
- The pendulum in the clock.
- A boy is spinning a rope with the stone at its end.
- In an experiment, two balls are dropped from a certain height which has their own momentum.
- A bike gains momentum when its gear is shifted.
- A car gains momentum when its brakes are removed at a slope.

**Law of conservation of momentum **

The law of conservation of momentum states that if no net external unbalanced force acts on a system, then the total momentum of all the bodies of the system before the collision will be equal to the total momentum of all the bodies of the system after the collision.

**Application of Law of conservation of momentum**

- A gun and a bullet mechanism. Both the rifle and the bullet are at rest before firing, hence the system’s overall momentum is zero. The bullet bursts out of the rifle and gains momentum as it is shot. The gun recoils to conserve the system’s momentum. After the gun is fired, the total momentum of the gun and the bullet will be zero, according to the law of conservation of momentum.
- Consider the third law of motion, which helps to describe the motion of an air-filled balloon. The balloon and the air inside it make a system in this situation. The system was at rest before we release the balloon, hence its initial momentum was zero. Air escapes from the balloon as soon as it is released, and it has momentum. The balloon travels in the opposite direction of the air streaming out to conserve momentum.

### The significance of momentum and its application

- Momentum can be used in various aspects of daily life like in airbags of the car. This uses the principles of momentum and impulse. When a person is involved in a crash, their momentum pushes them forward, causing them to collide with the steering wheel. By placing an airbag in the vehicle, a lower force is applied over a longer period of time and lowers the driver’s motion.
- For hydrodynamic force calculations, such as force acting on a gate or flow resistance in constant equilibrium flow, the momentum principle is always utilized. Hydraulic jumps are examples of other uses. For frictionless flow, a hydraulic jump was devised.
- In physics, momentum is used to define the relation between speed, mass, and direction. It also refers to the force required to bring items to a stop and keep them moving. It can also estimate how fast and which way objects would move after colliding.
- The conservation of momentum is used by rockets and jet engines. These machines obtain an equal and opposite momentum as the hot gases created by fuel combustion rush out with significant momentum. This momentum enables rockets and jet engines to travel at extremely high speeds.
- The link between momentum and force is quite useful. Change in velocity Δv can also be represented as a. Δt, as recalled from the kinematic equations.

### Conceptual Questions

**Question 1: What is the most important factor in momentum?**

**Answer:**

Direction is the most important factor in momentum.

**Question 2: State the law of conservation of momentum.**

**Answer:**

The law of conservation of momentum states that if no net external unbalanced force acts on a system, then the total momentum of all the bodies of the system before the collision will be equal to the total momentum of all the bodies of the system after the collision.

**Question 3: What can we find by momentum in the collusion of a moving object?**

**Answer:**

The direction of the object can be determined after the collusion by finding its momentum before collusion.

**Question 4: Which type of momentum has a fixed direction?**

**Answer:**

Linear momentum has fixed direction ideally (if there is no obstacle through which it can cause collusion) .

**Question 5: In real**–**life conditions, how does momentum stop?**

**Answer:**

Momentum can be stopped by,

- Putting obstacle (Collusion),
- Increasing the friction of the surface of path,
- Applying opposite force,
- Due to gravitation (natural).

**Question 6: What happens to an object in motion in space?**

**Answer:**

Gravity affects the movement of objects in space. Gravity is a powerful force that may alter the trajectory of objects in space, tug them off course, or even cause them to collide. So at some point they will come in contact with gravitation and will act accordingly.

### Sample Problems

**Question 1: A bicycle of 45 kg at a 20 km velocity is on the highway, what will be its momentum?**

**Solution: **

Given:

- m = mass of bicycle = 45kg
- v = velocity (speed) of bicycle = 20 m/s
Thus by using formula for momentum,

p = m × v

p = 45 × 20

p = 900 kg.m/s

**Question 2: A car has a momentum of 250 kg.m/s. What will be its momentum if its mass is twice mass?**

**Answer:**

Given,

- momentum (p) = 250 kg.m/s
Condition,

- Twice the mass of the car.
Thus, this changes the formula for momentum like,

p = 2(m × v)

The value of m × v is 250,

So,

p = 2 × 250

p = 500 kg.m/s

Thus if the mass was twice then the momentum will increase twice and p will be 500kg,m/s.