Internal forces in AP Physics C: Mechanics

Internal forces are forces that objects within a defined system exert on each other. By Newton's third law they come in equal and opposite pairs, so they sum to zero and cannot change the motion of the system's center of mass or its total momentum.

What are internal forces?

Internal forces are the forces that members of a system exert on each other. Whether a force counts as internal depends entirely on where you draw your system boundary. Two astronauts pushing off each other? If your system is "both astronauts," those pushes are internal. If your system is just one astronaut, the other astronaut's push is now an external force.

Here's the payoff. By Newton's third law, every internal force comes paired with an equal and opposite partner inside the same system. Add up all the internal forces and they cancel completely. That means internal forces can never accelerate the system's center of mass or change the system's total momentum. They can absolutely change the motion of individual pieces (an exploding firecracker sends fragments flying), and they can change the system's kinetic energy (a released spring adds KE). But the center of mass keeps doing whatever it was doing, as if the internal forces never happened.

Why internal forces matter in AP® Physics C: Mechanics

Internal forces live in Topic 2.3, Newton's Third Law, because the whole idea rests on third-law pairs canceling inside a system. But the concept is really a bridge. It's the reason momentum conservation works in Unit 4: when the net external force on a system is zero, internal forces alone can't change total momentum, so momentum is conserved through collisions and explosions. It's also the logic behind center-of-mass problems. Choosing a smart system boundary that turns messy forces into internal ones (which you can then ignore for center-of-mass motion) is one of the highest-leverage problem-solving moves in the whole course.

How internal forces connect across the course

Equal and opposite forces (Unit 2)

Internal forces always show up as third-law pairs. When satellite A pulls on satellite B with 50 N, B pulls back on A with 50 N. Inside the two-satellite system, those forces cancel, which is exactly why the net external force on the center of mass can be zero even while big forces act between the parts.

Conservation of momentum (Unit 4)

Internal forces are the entire reason momentum conservation exists. In an explosion or collision, the forces between fragments are huge but internal, so they cancel pairwise and total momentum stays fixed. A firecracker at rest explodes into three fragments, and the fragments' momenta must still add to zero.

Center of mass motion (Unit 4)

Only the net external force determines the acceleration of a system's center of mass (F_ext = M·a_cm). Two astronauts pushing off each other fly apart, but their center of mass stays put, because their push is internal to the astronaut system.

Tension and ideal pulleys (Unit 2)

When you treat two blocks connected over an ideal pulley as one system, the rope tension becomes internal and drops out of the equation for the system's acceleration. That's why the shortcut a = F_net,external / m_total works.

Are internal forces on the AP® Physics C: Mechanics exam?

Internal forces show up most often as a system-boundary trap. A classic MCQ stem gives two astronauts (say 70 kg and 90 kg) pushing off each other and asks what happens to the center of mass of the two-astronaut system. The answer is that it stays at rest, because the push is internal. Explosion problems are the same idea in disguise: a firecracker at rest breaks into fragments, and you use "internal forces conserve momentum" to find the missing fragment's velocity. Watch for the energy twist, too. A compressed spring between two blocks is internal, so momentum is conserved when it's released, but kinetic energy is NOT conserved (the spring adds energy). On FRQs, explicitly stating "the forces are internal to the system, so total momentum is conserved" is exactly the kind of justification that earns reasoning points.

Internal forces vs External forces

Internal forces act between objects inside your chosen system and always cancel in pairs. External forces come from outside the system boundary and are the only forces that can accelerate the center of mass. The trick is that the label isn't fixed. The same physical force flips from external to internal just by redrawing your system. Tension between two connected blocks is external if your system is one block, internal if your system is both.

Key things to remember about internal forces

• Internal forces are forces that objects inside a system exert on each other, and which forces count as internal depends on how you define the system.

• By Newton's third law, internal forces occur in equal and opposite pairs, so they always sum to zero within the system.

• Internal forces cannot change a system's total momentum or accelerate its center of mass; only external forces can do that.

• Internal forces CAN change the kinetic energy of a system, like a compressed spring or an explosion adding KE while momentum stays conserved.

• Choosing a system boundary that makes complicated forces internal (like tension in a pulley system) lets you ignore them and solve for the system's motion directly.

Frequently asked questions about internal forces

What are internal forces in AP Physics C?

Internal forces are forces that objects within a defined system exert on each other, like two astronauts pushing off one another or tension between two connected blocks. Because they form Newton's third law pairs, they cancel and can't change the system's total momentum or center-of-mass motion.

Do internal forces affect the center of mass?

No. Internal forces cancel in equal-and-opposite pairs, so they can't accelerate the center of mass. If two 70 kg and 90 kg astronauts at rest push off each other, both move, but the center of mass of the two-astronaut system stays exactly where it was.

What's the difference between internal and external forces?

Internal forces act between objects inside your system; external forces come from outside it. Only external forces can change the system's total momentum (F_ext = dp/dt). The same force can be either one depending on where you draw the system boundary.

Can internal forces change a system's kinetic energy?

Yes. Internal forces conserve momentum, not kinetic energy. A compressed spring between a 4.0 kg and a 6.0 kg block adds kinetic energy to the system when released, even though the total momentum stays zero.

Why is momentum conserved during an explosion?

Because the explosive forces between fragments are internal to the system. They cancel pairwise by Newton's third law, so a 2.0 kg firecracker at rest must have fragments whose momenta still add up to zero after it explodes.