Conservation of Momentum: The Unchanging Total
What is Momentum?
Before we can understand its conservation, we must first understand momentum itself. In everyday language, momentum is often used to describe something that is hard to stop once it gets going. In physics, this idea is made precise. Momentum is defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction.
Imagine a large, slow-moving truck and a small, fast-moving skateboarder. The truck has a large mass, and the skateboarder has a high velocity. Which one would be harder to stop? The answer depends on their momentum. A truck, even moving slowly, has immense momentum due to its large mass. A skateboarder, even moving very fast, has less momentum due to a smaller mass. Momentum helps us quantify this "amount of motion."
The Law of Conservation of Momentum
The law of conservation of momentum is one of the most powerful and universal laws in all of physics. It states that the total momentum of a closed system remains constant if no external net force acts on it. Let's break down the key terms:
- Closed System: A system that does not exchange matter with its surroundings and has no external forces acting on it. For example, two balls colliding on a frictionless table can be considered a closed system.
- External Net Force: A force from outside the system. If the net sum of all these external forces is zero, the system's total momentum is conserved.
This means that within such a system, momentum can be transferred from one object to another, but the total amount of momentum (adding up the momentum of all objects, taking direction into account) never changes. It is conserved.
Types of Collisions and Momentum
Collisions are a perfect playground for observing the conservation of momentum. While the total momentum is always conserved in a closed system, what happens to the kinetic energy[1] determines the type of collision. The table below summarizes the main types.
| Collision Type | What is Conserved? | What Happens? | Example |
|---|---|---|---|
| Elastic | Momentum and Kinetic Energy | Objects bounce off each other perfectly. No permanent deformation or heat generation. | Two billiard balls colliding. |
| Inelastic | Momentum only | Objects stick together or deform. Some kinetic energy is converted to other forms like sound, heat, or deformation. | A car crash where the cars crumple and stick together. |
| Perfectly Inelastic | Momentum only | Objects stick together and move as one single object after the collision. This is a specific case of an inelastic collision. | A bullet embedding itself into a block of wood. |
Momentum in Action: Real-World Scenarios
The conservation of momentum is not just a theoretical idea; it explains countless phenomena we see every day.
Example 1: Recoil of a Gun
When a bullet is fired from a gun, the gun exerts a forward force on the bullet, propelling it out of the barrel. According to Newton's Third Law, the bullet exerts an equal and opposite force on the gun. This is a closed system (gun + bullet) with no external forces initially. Before firing, the total momentum is zero. After firing, the bullet gains forward momentum. To keep the total momentum at zero, the gun must gain an equal amount of momentum in the opposite direction. This is the "kick" or recoil you feel.
Example 2: Rocket Propulsion
Rockets in space work on the same principle. They are a closed system (rocket + fuel). The rocket engine expels high-speed exhaust gases backward. This gives the exhaust gas a large backward momentum. To conserve momentum, the rocket must gain an equal amount of forward momentum, propelling it forward. This is how rockets maneuver in the vacuum of space where there is no air to push against.
Example 3: The Newton's Cradle
This classic desk toy perfectly demonstrates conservation of momentum and energy. When you lift and release one ball on the end, it swings down and collides with the others. The impact transfers momentum through the line of stationary balls, causing only the ball on the opposite end to swing out. If you lift two balls, two balls swing out on the other side. The total momentum and (in an ideal, frictionless world) kinetic energy are conserved throughout the process.
Common Mistakes and Important Questions
A: Momentum is only conserved for a closed system with no external net force. A rolling ball is not a closed system. External forces like friction from the ground and air resistance act on it. These forces slow the ball down, transferring its momentum to the Earth. The momentum of the ball-Earth system is conserved, but since the Earth is so massive, its change in velocity is imperceptible.
A: They are two separate, fundamental laws. Conservation of momentum is a vector law concerned with mass and velocity. Conservation of energy is a scalar law concerned with the different forms energy can take (kinetic, potential, heat, etc.). In an elastic collision, both are conserved. In an inelastic collision, momentum is conserved, but some kinetic energy is transformed into other forms of energy and is therefore not "conserved" as kinetic energy.
A: Yes. An object at rest has zero momentum ($ \vec{v} = 0 $), but it can have potential energy, like a book on a high shelf. An object can also have momentum but no kinetic energy, but this is a trickier concept. If the total momentum of a system is zero (objects moving in opposite directions), the system's kinetic energy can be non-zero, but a single object with mass must have velocity to have momentum, and thus must have kinetic energy.
Footnote
[1] Kinetic Energy (KE): The energy an object possesses due to its motion. It is given by the formula $ KE = \frac{1}{2}mv^2 $ and is a scalar quantity, meaning it has magnitude but no direction.