Momentum
A vector quantity representing the "quantity of motion" of an object. Symbol: p. Equal to mass times velocity (p = mv). SI unit: kg·m/s.
FoundationVector Quantity (in Unit 4)
Momentum, impulse, and force are all vectors — they have BOTH magnitude AND direction. This matters because momenta in opposite directions can cancel. When adding momenta, treat opposite directions as opposite signs.
FoundationLinear Momentum
p = mv. The momentum of an object due to its translational motion. A vector — same direction as the velocity. Often just called "momentum" in this unit. SI unit: kg·m/s (or N·s).
4.1 Linear MomentumDirection of Momentum
Momentum always points in the same direction as the velocity. A car moving east has eastward momentum; if it slows down, the momentum magnitude decreases but direction stays. If it reverses, momentum flips direction.
4.1 Linear MomentumCollision
An interaction in which two or more objects exert large forces on each other for a brief time. The internal forces are MUCH larger than any external forces, so collision problems usually treat external forces as negligible during the collision itself.
4.1 Linear MomentumExplosion
An interaction where internal forces push objects within a system apart. Like a collision in reverse. Momentum is conserved: if the system was at rest, momentum is still zero after, so fragments move in opposite directions.
4.1 Linear MomentumObject Model (in Collisions)
A simplification that treats each colliding object as a single particle with mass and velocity. Works because we only care about the initial and final states — not what happens during the brief collision itself.
4.1 Linear MomentumChange in Momentum (Δp)
Δp = p_f − p_i. The difference between final and initial momenta. A vector. Since momentum is a vector, a change in DIRECTION (even at the same speed) is still a change in momentum.
4.2 ImpulseImpulse
J = F_avg · Δt. The product of the average force on an object and the time interval over which it acts. A vector quantity in the same direction as the net force. SI unit: N·s (which equals kg·m/s).
4.2 ImpulseImpulse-Momentum Theorem
J = Δp. The impulse delivered to a system equals its change in momentum. This is just Newton's second law in a different form — it connects forces to momentum changes through time.
4.2 ImpulseNewton's Second Law (momentum form)
F_net = Δp/Δt. The net force equals the rate of change of momentum. For constant mass, this reduces to F = ma. It also explains why catching an egg with a soft hand reduces force — longer Δt means smaller F for the same Δp.
4.2 ImpulseForce-Time Graph
A graph of net force vs. time. The AREA under the curve equals the impulse (and therefore the change in momentum). Useful for non-constant forces — like the force of a baseball bat on a ball, which spikes and then drops.
4.2 ImpulseMomentum-Time Graph
A graph of momentum vs. time. The SLOPE at any instant equals the net force at that moment. Constant momentum → zero slope → zero net force (Newton's first law).
4.2 ImpulseAverage Force
F_avg = Δp/Δt = J/Δt. The "smoothed-out" force during an interaction. Doubling the time interval (e.g., bending your knees when landing) halves the average force for the same momentum change.
4.2 ImpulseConservation of Linear Momentum
When the net external force on a system is zero, total momentum is constant: p_i,total = p_f,total. This is one of the most powerful tools in physics — it works even when forces are too complicated to analyze in detail.
4.3 ConservationClosed (Isolated) System
A system with no momentum transfer from outside. The net external force is zero, so total momentum is conserved. Choosing the right system is half the battle on conservation problems.
4.3 ConservationTotal Momentum of a System
The vector sum of the momenta of all objects in the system: p_total = p_1 + p_2 + p_3 + ... Treat opposite directions as opposite signs in 1D. In 2D, add by components (we won't compute these in detail in AP1).
4.3 ConservationCenter-of-Mass Velocity
v_cm = (m₁v₁ + m₂v₂ + ...) / (m₁ + m₂ + ...). The velocity of the system's center of mass. In the absence of net external force, v_cm is CONSTANT — even if individual objects collide, accelerate, or change speeds.
4.3 ConservationInternal vs External Forces (momentum)
Internal forces (between objects within the system) come in Newton's-third-law pairs that cancel — they can never change total momentum. Only EXTERNAL forces can. This is why colliding cars don't change combined momentum on a frictionless track.
4.3 ConservationNewton's Third Law (momentum version)
When two objects interact, the impulse one exerts on the other is equal and opposite to the impulse the other exerts back. This means changes in momentum come in equal and opposite pairs — exactly why total momentum is conserved.
4.3 ConservationElastic Collision
A collision in which the total kinetic energy of the system is the same before and after (KE_i = KE_f). Momentum is also conserved. Idealized — billiard balls, atoms, and bouncy carts come close.
4.4 CollisionsInelastic Collision
A collision in which the total kinetic energy DECREASES (KE_f < KE_i). Some KE is converted to other forms — heat, sound, or deformation. Momentum is STILL conserved. Most real-world collisions are inelastic.
4.4 CollisionsPerfectly Inelastic Collision
An inelastic collision where the objects stick together after impact and move with a single common velocity. This is the EXTREME case — the MOST kinetic energy is lost. Momentum is still conserved: (m₁v₁ + m₂v₂) = (m₁ + m₂)v_f.
4.4 CollisionsKinetic Energy in Collisions
KE = ½mv². Calculate KE before and after to determine if a collision is elastic (same KE) or inelastic (less KE). For any collision: KE_f / KE_i tells you the fraction "preserved."
4.4 CollisionsEnergy Transformation in Inelastic Collisions
The KE that "disappears" in an inelastic collision isn't destroyed — it's converted to thermal energy (heat), sound, light, or work done deforming the objects. Total energy is still conserved; it just leaves the kinetic form.
4.4 CollisionsOne-Dimensional Collision
A collision where all motion is along a single line. The simplest case for AP Physics 1. Treat directions as positive or negative signs. The main exam scenario you'll encounter.
4.4 CollisionsTwo-Dimensional Collision
A collision where objects move in a plane (like two cars colliding at an intersection). AP Physics 1 expects only qualitative/semiquantitative analysis — you may have to reason about directions without solving full vector equations.
4.4 CollisionsSI Unit of Momentum (kg·m/s)
Kilograms times meters per second. Equivalent to N·s (newton-seconds), because impulse and momentum share units (since J = Δp).
4.1 Linear MomentumSI Unit of Impulse (N·s)
Newton-seconds. Equal to kg·m/s — same as momentum. This is no coincidence: the impulse-momentum theorem says they're the same physical quantity.
4.2 Impulse