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## Introduction

Hey it's a me again @drifter1! Today we continue with **Physics** and more specifically the branch "**Classical Mechanics**" to start talking about **Momentum**. So, without further ado, let's get straight into it!

## Momentum

Talking about moving objects, momentum is equal to the**product of the mass of the object and its velocity**. It's a

**vector quantity**(has magnitude and direction) with the same direction as the velocity. Based on Newton's second law of motion

**the change in momentum is equal to the force that acts on an object**. But, what exactly that this mean for us? Well, momentum is the quantity that shows us

*how much*is moving (mass) and

*how fast*it moves (velocity). It can be defined as "mass in motion" meaning that it somewhat shows us

*how hard*(how much force) we have to apply to stop an object.

Mathematically, we write momentum as:

The symbol that is used to describe momentum is the lower case 'p'. From the quantities that take place in the previous equation we understand that

**the S.I. unit of momentum is kg ·m/s**.

Newton's 2nd law looks like this:

Knowing that the mass is a constant and that the change of velocity over time is equal to the quantity known as acceleration (a), we can write the

**commonly known 2nd law equation**:

### Example

Determine the momentum in the following cases:- 80-kg person moving at 3 m/s
- 2000-kg car moving at 30m/s
- 40-kg kid running at 5 m/s

**1.**

**2.**

**3.**

**Note:**You can see that the kid has a smaller momentum, even though its faster than the person, because it has less mass and so a smaller product.

## Conservation of Momentum

An important and very powerful law in Physics is the "law of momentum conservation". Based on**Newton's third law**(each action has a reaction - the forces are equal in magnitude and opposite in direction), in collisions between two objects, the

**momentum changes**are equal in magnitude and opposite in direction,

**conserving the total momentum of the isolated system**.

Mathematically, the conservation looks like this:

This equation contains the momentum p1 of an object 1 and the momentum p2 of an object 2. Supposing that these objects are in an isolated system, a collision between object 1 and object 2 would cause an equal in magnitude but opposite in direction change in momentum, therefore keeping the total momentum of the system (p1 + p2) constant.

This of course applies to any number of objects, which are in an isolated system.

**Generalizing**it, for any initial and any final state of such an system and N objects, we can write:

Various types of collisions with examples and other very interesting topics around momentum and its conservation will be covered in follow-up articles!

## RESOURCES:

### References

- https://www.britannica.com/science/momentum
- https://www.physicsclassroom.com/Class/momentum/u4l1a.cfm
- https://www.physicsclassroom.com/class/momentum/Lesson-2/Momentum-Conservation-Principle
- http://scienceworld.wolfram.com/physics/ConservationofMomentum.html
- https://www.khanacademy.org/science/ap-physics-1/ap-linear-momentum/conservation-of-momentum-and-elastic-collisions-ap/a/what-is-conservation-of-momentum

### Images

Mathematical equations used in this article, where made using quicklatex.

## Previous articles of the series

### Rectlinear motion

- Velocity and acceleration in a rectlinear motion -> velocity, accelaration and averages of those
- Rectlinear motion with constant accelaration and free falling -> const accelaration motion and free fall
- Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity
- Rectlinear motion exercises -> examples and tasks in rectlinear motion

### Plane motion

- Position, velocity and acceleration vectors in a plane motion -> position, velocity and accelaration in plane motion
- Projectile motion as a plane motion -> missile/bullet motion as a plane motion
- Smooth Circular motion -> smooth circular motion theory
- Plane motion exercises -> examples and tasks in plane motions

### Newton's laws and Applications

- Force and Newton's first law -> force, 1st law
- Mass and Newton's second law -> mass, 2nd law
- Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction
- Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications
- Contact forces and friction -> contact force, friction
- Dynamics of Circular motion -> circular motion dynamics, applications
- Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications
- Contact force and friction examples -> exercises in force and friction
- Circular dynamic and vertical circle motion examples -> exercises in circular dynamics
- Advanced Newton law examples -> advanced (more difficult) exercises

### Work and Energy

- Work and Kinetic Energy -> Definition of Work, Work by a constant and variable Force, Work and Kinetic Energy, Power, Exercises
- Conservative and Non-Conservative Forces -> Conservation of Energy, Conservative and Non-Conservative Forces and Fields, Calculations and Exercises
- Potential and Mechanical Energy -> Gravitational and Elastic Potential Energy, Conservation of Mechanical Energy, Problem Solving Strategy & Tips
- Force and Potential Energy -> Force as Energy Derivative (1-dim) and Gradient (3-dim)
- Potential Energy Diagrams -> Energy Diagram Interpretation, Steps and Example
- Potential Energy Diagrams -> Internal Energy, Internal Work

## Final words | Next up

This is actually it for today's post! Next time we will get into Collisions...

See ya!

Keep on drifting!