← Back to CoursesNewtonian Mechanics: Beginner

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Momentum and Impulse

Manual: General · Subject: Newtonian Mechanics

Introduce momentum conservation and the role of impulse in changing motion.

A New Way to Measure Motion

Momentum

Momentum is defined as p⃗=mv⃗\vec{p} = m\vec{v}. It combines mass and velocity, so a heavy fast object has more momentum than a light slow one.

Impulse

Impulse is force applied over time, and it changes momentum: J⃗=Δp⃗\vec{J} = \Delta \vec{p}. For constant force, J⃗=F⃗Δt\vec{J} = \vec{F}\Delta t.

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Why impulse matters

A small force acting for a long time can change momentum as much as a large force acting briefly.

Conservation of momentum

If no external net force acts on a system, total momentum stays constant. This is extremely useful in collisions and explosions.

What is momentum?

What does impulse equal?

Momentum vs. impulse

Momentum

  • State of motion
  • p⃗=mv⃗\vec{p} = m\vec{v}
  • Usually conserved in isolated systems

Impulse

  • Change caused by force over time
  • J⃗=Δp⃗\vec{J} = \Delta \vec{p}
  • Explains how momentum changes

Momentum problem strategy

  1. 1

    Step 1: Define the system clearly.

  2. 2

    Step 2: Check whether external forces can be neglected.

  3. 3

    Step 3: Write initial and final total momentum.

  4. 4

    Step 4: Use conservation of momentum if appropriate.