Conservation of Momentum

Conservation of momentum states that if no net external force acts on a system (a closed system), the total momentum of that system stays constant, so the total momentum before a collision or explosion equals the total momentum after.

What is Conservation of Momentum?

Momentum is mass in motion, calculated as p = mv. Conservation of momentum says that when a system is closed, meaning no net external force pushes on it from outside, the system's total momentum never changes. Objects inside the system can crash, stick together, push off each other, or explode apart, and the individual momenta will shuffle around. But add them all up as vectors and the total before always equals the total after.

The whole game in AP Physics 1 is choosing your system wisely. If you draw your system boundary around BOTH colliding objects, the forces they exert on each other become internal forces, and internal forces can never change total momentum (Newton's third law guarantees they cancel). That's why Topic 5.3 is literally called Open and Closed Systems. Friction from the floor or a hand pushing from outside? Those are external forces, and they break the conservation. The same logic extends to rotation in Topic 7.4, where total angular momentum is conserved when no net external torque acts.

Why Conservation of Momentum matters in AP Physics 1

Conservation of momentum anchors Topic 5.3 (Open and Closed Systems: Momentum) and its rotational twin shows up in Topic 7.4 (Conservation of Angular Momentum). It's also part of a bigger pattern the course keeps hammering. The CED's essential knowledge for SHM (under 7.4.A) says the total energy of an oscillating system is constant, and momentum conservation is the same idea applied to a different quantity. Physics keeps a few totals fixed, and your job is to figure out which one applies. On the exam, momentum conservation is often the ONLY tool that works, because collision forces are messy and short-lived. You can't track them with F = ma, but you can compare total momentum before and after without knowing anything about the forces in between.

How Conservation of Momentum connects across the course

Impulse (Unit 5)

Impulse is the flip side of the same coin. Impulse (J = FΔt) is how an external force changes a system's momentum. Conservation of momentum is just the special case where the net external impulse is zero. If you can name the external force, you can explain exactly why momentum is or isn't conserved.

Elastic and Inelastic Collisions (Unit 5)

Momentum is conserved in BOTH types of collision. The difference is kinetic energy. Elastic collisions keep kinetic energy; inelastic collisions (especially perfectly inelastic ones where objects stick) lose kinetic energy to heat and deformation. Momentum conservation gives you the equation; the collision type tells you whether you get a second one.

Conservation of Angular Momentum (Unit 7)

Topic 7.4 is the rotational remix. Swap force for torque and momentum for angular momentum, and the rule reads identically. With no net external torque, total angular momentum stays constant. That's why a spinning skater speeds up when she pulls her arms in, even though nothing pushed her.

Torque and Force Diagrams (Unit 5)

Learning objectives 5.3.A and 5.3.B have you identify and describe the torques on a rigid system using force diagrams. That skill feeds directly into conservation arguments. Before you can claim angular momentum is conserved, you have to draw the diagram and show the net external torque is zero.

Is Conservation of Momentum on the AP Physics 1 exam?

Momentum conservation is FRQ gold. The 2021 Long FRQ Q3 put a student on a smooth (frictionless) surface pushing a disk away, and the frictionless detail is the giveaway that the student-plus-disk system is closed, so the student recoils with momentum equal and opposite to the disk's. The 2025 FRQ Q1 had a cart of mass m_c collide with a block of mass 5m_c, a classic before-and-after setup where you write p_before = p_after and solve. Expect to do three things. First, justify in writing WHY momentum is conserved by pointing to the absence of net external force on your chosen system. Second, set up the conservation equation with correct signs, since momentum is a vector and directions matter. Third, decide whether kinetic energy is also conserved (only if the collision is elastic). MCQs love asking which quantities are conserved in a perfectly inelastic collision; the answer is momentum yes, kinetic energy no.

Conservation of Momentum vs Conservation of Energy

These are separate laws with separate conditions, and the exam punishes mixing them up. Momentum is conserved whenever the net external FORCE on the system is zero, even in violent, sticky, energy-wasting collisions. Mechanical energy is conserved only when no nonconservative forces (like friction or deformation) drain it. In a perfectly inelastic collision, momentum is fully conserved while kinetic energy drops. If you write 'energy is conserved so the velocities are equal' on a collision FRQ, you've used the wrong law.

Key things to remember about Conservation of Momentum

• In a closed system with no net external force, total momentum before an event equals total momentum after, no matter how chaotic the event is.

• Internal forces, like the forces colliding objects exert on each other, can never change a system's total momentum because Newton's third law pairs cancel.

• Momentum is conserved in every type of collision, but kinetic energy is only conserved in elastic collisions.

• Momentum is a vector, so set a positive direction first and keep your signs straight when objects move opposite ways.

• On FRQs, earn the justification point by stating that the net external force on your chosen system is zero, often signaled by words like 'frictionless' or 'smooth surface.'

• The same conservation logic applies to rotation in Topic 7.4, where angular momentum stays constant when the net external torque is zero.

Frequently asked questions about Conservation of Momentum

What is conservation of momentum in AP Physics 1?

It's the principle that the total momentum of a closed system (one with no net external force) stays constant. So in a collision between two carts, the sum of their momenta before impact equals the sum after, even if they stick together.

Is momentum conserved in an inelastic collision?

Yes. Momentum is conserved in ALL collisions as long as the system is closed. What an inelastic collision loses is kinetic energy, which gets converted to heat, sound, and deformation. The 2025 FRQ with a cart hitting a 5m_c block tested exactly this distinction.

How is conservation of momentum different from conservation of energy?

Momentum conservation needs zero net external force; energy conservation needs no nonconservative forces draining mechanical energy. A perfectly inelastic collision conserves momentum but not kinetic energy, which is why collision problems usually start with the momentum equation, not the energy equation.

How do I know if a system is closed on an AP Physics FRQ?

Look for the giveaway phrases. 'Frictionless surface,' 'smooth surface,' or 'negligible friction' mean no horizontal external force acts during the interaction, so momentum is conserved. The 2021 FRQ put a student on a smooth surface for exactly this reason.

Does conservation of momentum apply to rotation?

Yes, as conservation of angular momentum, covered in Topic 7.4. The condition just changes from zero net external force to zero net external torque. A spinning object that pulls mass toward its axis spins faster because angular momentum L stays fixed while rotational inertia drops.