AP Physics 1 Big Ideas Review

Before any analysis, you must define what you are studying. An object is treated as a point mass when internal structure does not matter. A system is a defined collection of objects, and where you draw the system boundary determines whether forces are internal or external and whether energy or momentum crosses the boundary.

• System boundary: The imaginary line separating the system from its surroundings; forces crossing it are external, forces within it are internal.
• Internal structure: Properties like mass distribution and charge that matter when analyzing rotation, collisions, or electric interactions.
• Point mass approximation: Treating an extended object as if all its mass is at one point, valid when rotation and internal structure are irrelevant.

Every interaction between two objects can be described as a force. Forces come in contact types (normal, friction, tension, spring) and long-range types (gravity, electric). Newton's third law means every force has an equal and opposite reaction force on the other object. Free-body diagrams are the primary tool for representing this Big Idea.

• Contact force: A force that requires physical contact: normal force, static friction, kinetic friction, tension, spring force.
• Long-range force: A force that acts across a distance without contact: gravity and electric force in AP Physics 1.
• Newton's third law pair: Two forces that are equal in magnitude, opposite in direction, act on different objects, and are of the same type.

Net force determines acceleration. This Big Idea is Newton's second law in its broadest form: it applies to linear motion (a = Fnet/m), rotational motion (alpha = tau_net/I), and circular motion (Fnet = mv^2/r toward center). Equilibrium is the special case where net force and net torque are both zero.

• Newton's second law (linear): a = Fnet/m; the acceleration of an object equals the net force divided by its mass.
• Rotational analog: alpha = tau_net/I; angular acceleration equals net torque divided by rotational inertia.
• Centripetal acceleration: ac = v^2/r; always directed toward the center of the circular path, produced by the net inward force.

Interactions transfer energy between objects or convert it between forms. The work-energy theorem (W_net = delta KE) connects force and displacement to kinetic energy change. Potential energy (gravitational: mgh, spring: 1/2 kx^2) is stored in systems. Power is the rate of energy transfer: P = W/t = Fv.

• Work-energy theorem: The net work done on an object equals its change in kinetic energy: W_net = delta KE.
• Gravitational PE: Ug = mgh; stored energy due to position in a gravitational field, defined relative to a chosen reference height.
• Elastic PE: Us = 1/2 kx^2; energy stored in a compressed or stretched spring, where x is displacement from equilibrium.
• Power: P = W/t = Fv; the rate at which work is done or energy is transferred.

Momentum, energy, and angular momentum are conserved in closed systems. Momentum conservation (p_total = constant when Fnet_ext = 0) governs collisions and explosions. Angular momentum conservation (L = I*omega = constant when tau_net_ext = 0) governs spinning systems. Energy is always conserved, but mechanical energy is only conserved when no non-conservative forces do work.

• Linear momentum: p = mv; conserved when no net external force acts on the system.
• Impulse-momentum theorem: J = Fnet * delta t = delta p; impulse equals the change in momentum.
• Angular momentum: L = I * omega; conserved when no net external torque acts on the system.
• Elastic vs. inelastic collision: Elastic: both momentum and kinetic energy conserved. Inelastic: momentum conserved, kinetic energy not fully conserved.

Waves transfer energy and momentum without permanently moving mass. Mechanical waves require a medium; wave speed depends on medium properties. Key relationships: v = f*lambda, and for a string v = sqrt(T/mu). Superposition produces interference (constructive and destructive) and standing waves. Sound is a longitudinal mechanical wave; the Doppler effect shifts observed frequency when source or observer moves.

• Wave speed equation: v = f * lambda; wave speed equals frequency times wavelength.
• Superposition principle: When two waves overlap, the net displacement at any point is the sum of the individual displacements.
• Standing wave: A pattern formed by superposition of two identical waves traveling in opposite directions; nodes are points of zero displacement.
• Doppler effect: The observed frequency of a wave changes when the source and observer move relative to each other; approaching increases frequency, receding decreases it.

SHM occurs when a restoring force is proportional to displacement from equilibrium (F = -kx for springs, F = -mg*sin(theta) approximated as -mg*theta for small-angle pendulums). Period depends on system properties, not amplitude. Energy oscillates between kinetic and potential. SHM connects directly to Big Ideas 4 and 5 through energy conservation.

• Restoring force: A force directed back toward equilibrium, proportional to displacement: F = -kx.
• Period of a mass-spring system: T = 2*pi*sqrt(m/k); depends on mass and spring constant, not amplitude.
• Period of a simple pendulum: T = 2*pi*sqrt(L/g); depends on length and gravitational field strength, not mass or amplitude (for small angles).
• Energy in SHM: Total mechanical energy E = 1/2 kA^2 is constant; KE is maximum at equilibrium, PE is maximum at maximum displacement.