Linear Momentum and its Conservation

What is Momentum?

Momentum is a measure of how much "motion" an object has. It depends on two things: how heavy the object is (its mass) and how fast it's moving (its velocity).

The formula for momentum is:

p = mv

Where:

• p = momentum (measured in kg m s⁻¹ or N s)
• m = mass (measured in kg)
• v = velocity (measured in m s⁻¹)

Important: Momentum is a vector quantity, which means it has both size (magnitude) and direction. If an object moves to the right, its momentum is positive; if it moves to the left, its momentum is negative.

The Principle of Conservation of Momentum

The principle of conservation of momentum states:

In simpler terms: In an isolated system (where no outside forces interfere), momentum doesn't just disappear or appear out of nowhere — it stays the same overall.

Mathematically, this is written as:

Total momentum before = Total momentum after

Or:

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

Where:

• m₁ and m₂ = masses of the two objects
• u₁ and u₂ = initial velocities (before collision)
• v₁ and v₂ = final velocities (after collision)

What is an "isolated system"?

An isolated system (also called a closed system) is one where no external forces act on the objects involved. External forces are forces from outside the system, like friction with the ground or a push from someone's hand. Internal forces are forces between the objects in the system, like when two objects push on each other during a collision.

Key Point: If external forces act (like friction), momentum may not be conserved. But in most collision problems, we assume the system is isolated for simplicity.