Inside This Unit: The Full Breakdown
Momentum covers linear momentum, impulse, and collisions. The impulse-momentum theorem and conservation of momentum provide powerful tools for analyzing interactions between objects, especially collisions and explosions.
Why it matters
Momentum conservation is a fundamental principle tested heavily on AP Physics 1. You must analyze elastic and inelastic collisions, apply the impulse-momentum theorem, and understand how momentum and energy conservation work together. These problems appear regularly in both multiple choice and free response.
Key concepts
- Linear momentum is p = mv, a vector quantity. The total momentum of a system is conserved when no net external force acts on it.
- Impulse (J = FΔt = Δp) equals the change in momentum. The area under a force-time graph gives the impulse.
- In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, momentum is conserved but kinetic energy is not.
- In perfectly inelastic collisions, the objects stick together and maximum kinetic energy is lost.
Momentum and Impulse
Momentum (p = mv) is a vector quantity that describes the "quantity of motion" of an object. A fast-moving car has large momentum; a slow-moving bicycle has small momentum. Newton's second law can be rewritten as ΣF = Δp/Δt — the net force equals the rate of change of momentum. Impulse is defined as J = FΔt (force multiplied by the time interval over which it acts), and the impulse-momentum theorem states J = Δp. This explains why airbags save lives: they increase the time of collision, reducing the force for the same momentum change. On a force-time graph, the impulse equals the area under the curve. For variable forces, this area must be calculated geometrically or by integration.
Conservation of Momentum
The law of conservation of momentum states that if no net external force acts on a system, the total momentum of the system remains constant: p_i = p_f. This law applies to systems of objects, not individual objects. To use it, define your system to include all interacting objects. Internal forces (forces between objects within the system) transfer momentum between objects but do not change the total. External forces (forces from outside the system) do change total momentum. Conservation of momentum is especially powerful for collisions and explosions, where the interaction forces are internal. In two-dimensional collisions, momentum is conserved independently in both the x and y directions.
Types of Collisions
Collisions are classified by what happens to kinetic energy. In elastic collisions, both momentum and kinetic energy are conserved — objects bounce off each other without any energy loss to deformation, sound, or heat. Elastic collisions are ideal; they occur approximately in billiard balls and atomic-scale interactions. In inelastic collisions, momentum is conserved but kinetic energy is not — some kinetic energy is converted to other forms (thermal, sound, deformation). In perfectly inelastic collisions, the objects stick together after impact, and the maximum possible kinetic energy is lost. To determine how much kinetic energy is lost, calculate KE before and after separately using ½mv² for each object. The "lost" energy is converted to internal energy of the objects.
AP exam tip
On the AP exam, conservation of momentum applies in all collisions (elastic and inelastic). Conservation of kinetic energy applies ONLY in elastic collisions. Always start collision problems by writing p_before = p_after, then check whether energy is also conserved to classify the collision type.
Connections to other units
- Unit 2 (Dynamics): Newton's second law in the form F = Δp/Δt connects force directly to momentum change.
- Unit 4 (Energy): Elastic collisions conserve both momentum and kinetic energy; inelastic collisions conserve only momentum.
- Unit 7 (Torque): Angular momentum (L = Iω) is the rotational analog of linear momentum.
