AP Physics C: Mechanics Unit 2 Notes — Newton’s Laws of Motion

Newton’s First Law

If the net external force on an object is zero, its velocity remains constant (it stays at rest or moves in a straight line at constant speed).

Net Force (ΣF)

The vector sum of all external forces acting on an object; determines whether the object accelerates.

Constant Velocity

Motion with unchanging speed and unchanging direction; implies zero acceleration (a = 0), not necessarily that no forces act.

Inertia

The tendency of an object to resist changes in its motion; in Newtonian mechanics, it is quantified by mass (more mass → harder to accelerate).

Equilibrium (in Newton’s Laws problems)

A situation with zero acceleration; forces may act but they balance so that ΣF = 0 (often treated via ΣFx = 0 and ΣFy = 0).

Inertial Reference Frame

A non-accelerating frame (or one where Newton’s laws hold to good approximation) in which objects with ΣF = 0 move at constant velocity.

Non-Inertial (Accelerating) Frame

A reference frame that accelerates, where objects may appear to accelerate without a real net force unless fictitious forces are introduced.

Fictitious Force

An apparent force introduced when analyzing motion from a non-inertial reference frame to account for observed acceleration in that frame.

Newton’s Second Law

The net external force on an object equals mass times acceleration: Σ⃗F = m⃗a (vectors).

Component Form of Newton’s Second Law

Writing forces and acceleration in chosen axes: ΣFx = max and ΣFy = may, which is how most problems are solved.

Free-Body Diagram (FBD)

A sketch that isolates a chosen object/system and shows all external forces acting on it, used to apply ΣFx = max and ΣFy = may correctly.

External Forces

Forces acting on the chosen object/system from outside it; only these appear on a correct FBD and determine ΣF for that object/system.

Weight (W)

The gravitational force on an object near Earth’s surface, magnitude W = mg, directed downward (toward Earth’s center).

Normal Force (N)

A contact force exerted by a surface, perpendicular to the surface; its magnitude adjusts to satisfy constraints and is not automatically equal to mg.

Tension (T)

A pulling force transmitted through an ideal rope/string; acts along the rope and pulls away from the object (ideal rope cannot push).

Static Friction (fs)

Friction that prevents slipping; its magnitude adjusts as needed up to a maximum: 0 ≤ fs ≤ μsN.

Maximum Static Friction

The largest possible static friction force before slipping occurs, equal to fs,max = μsN.

Kinetic Friction (fk)

Friction when surfaces slide relative to each other; magnitude fk = μkN and it opposes the relative motion.

Friction Direction Rule

Friction acts along the surface opposing relative motion (or impending motion), not necessarily opposing the applied force.

Apparent Weight

The “weight” a scale reads; equal to the normal force on a person (N), which can differ from mg when accelerating (e.g., elevator motion).

Newton’s Third Law

For every force A exerts on B, B simultaneously exerts an equal-magnitude, opposite-direction force on A: F⃗A→B = −F⃗B→A.

Action–Reaction Pair

A Newton’s Third Law pair: equal and opposite forces from the same interaction that act on different objects (so they do not cancel on one object).

Internal Forces (in a System)

Forces between objects within a chosen system; they cancel in the system’s net force calculation due to Newton’s Third Law.

Incline Weight Components

For an incline at angle θ, the weight components are mg sinθ parallel to the plane (down the slope) and mg cosθ perpendicular to the plane.

Hooke’s Law (Spring Force)

For an ideal spring, the spring force magnitude is proportional to displacement: Fs = kx, directed opposite the displacement from equilibrium.