Compression, Rebound, and Recoil: A Conceptual Study of Momentum and Energy

​In Chapter 10–4 of The Feynman Lectures on Physics, Richard Feynman develops a conceptual analysis of momentum and energy through the study of collisions and related interactions. Rather than relying on mathematical formalism, the discussion emphasises physical interpretation and symmetry arguments. This approach is especially effective at the undergraduate level, where the goal is to understand not only what physical laws state, but why they must hold across a wide range of situations.

The chapter begins by contrasting simple collisions in which bodies stick together or separate after an explosion with more general cases in which bodies rebound. In these latter situations, the key physical insight is that collisions are dynamic processes involving temporary energy storage. When two bodies collide and rebound, they do not instantly reverse direction. Instead, there is a brief interval during which both bodies are in contact, compressed, and momentarily at rest. At this instant of maximum compression, the original motion has ceased, and the energy associated with that motion is stored internally, much like energy stored in a compressed spring.

This internal storage of energy highlights an important distinction between momentum and kinetic energy. Momentum is conserved throughout the interaction, including during the moment of compression, whereas kinetic energy need not be. During compression, kinetic energy is converted into other forms of energy associated with deformation of the bodies. What happens next depends on the physical properties of the materials involved. If the bodies are highly elastic, most of the stored energy is returned to kinetic form as the bodies separate. If the bodies are inelastic, much of that energy is irreversibly transformed into heat and internal vibrations.

Feynman uses this discussion to introduce the concept of elastic and inelastic collisions. In an ideal elastic collision, the bodies separate with the same speeds they had before the collision. This outcome is not guaranteed by momentum conservation alone. Momentum conservation determines how velocities are related between interacting bodies, but the recovery of the original speeds requires that kinetic energy also be conserved. The distinction is subtle but crucial: momentum conservation explains the symmetry of motion between the bodies, while energy conservation determines the magnitude of the motion after the interaction.

The role of symmetry is especially clear in collisions between bodies of equal mass. When two such bodies approach each other with equal speeds, symmetry demands that they separate in the same manner. Feynman extends this reasoning by changing the observer’s frame of reference. By analyzing the collision from a frame moving with one of the bodies, it becomes evident that, in an elastic collision between equal masses, the bodies exchange velocities. This result, which can be demonstrated experimentally, reinforces the idea that conservation laws are independent of the observer’s motion and that changing reference frames can simplify physical reasoning.

The lecture also emphasizes that perfectly elastic collisions are most nearly realized in systems without internal complexity. Objects with internal structures—such as gears, flexible components, or frictional elements—provide mechanisms for energy to be trapped internally as heat or vibration. By contrast, very simple systems have few ways to absorb energy internally. This explains why collisions between atoms and molecules in a gas are treated as elastic to a very high degree of accuracy. Although such collisions are not perfectly elastic, the small energy losses involved are rare and negligible for most practical purposes.

Beyond mechanical collisions, Feynman broadens the discussion to include interactions such as magnetic repulsion. When two magnets repel each other without touching, the interaction still mirrors the behavior of elastic collisions. One object can come to rest while transferring its motion to the other, again illustrating momentum conservation without direct contact. This reinforces the idea that momentum exchange does not require physical contact but only interaction.

Finally, the lecture connects these principles to rocket propulsion. A rocket accelerates by ejecting mass at high speed, causing the remaining body to recoil in the opposite direction. The essential point is that motion arises from momentum conservation, not from interaction with the surrounding air. This example demonstrates the power of conservation laws: even without detailed knowledge of the internal processes driving the ejection, one can predict the rocket’s motion based solely on momentum balance.

Overall, Chapter 10–4 presents momentum and energy as complementary but distinct concepts. Momentum conservation provides robust predictions that hold regardless of the details of an interaction, while energy considerations explain the qualitative differences between elastic and inelastic processes. Feynman’s analysis shows that a deep understanding of physics emerges not from formulas alone, but from careful attention to physical mechanisms, symmetry, and conservation principles.