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!
MomentumTalking 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:
ExampleDetermine 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
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 MomentumAn 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!
Mathematical equations used in this article, where made using quicklatex.
Previous articles of the series
- 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
- 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...
Keep on drifting!