AP Physics C: Mechanics — Unit 2 Newton’s Laws (Concepts, Methods, and Worked Problems)

Force

An interaction (push/pull) between objects or fields that can change an object’s motion (velocity) or shape; treated as a vector in mechanics.

Vector (force as a vector)

A quantity with magnitude and direction; forces add as vectors to produce a net force.

Contact force

A force that requires physical contact between objects (e.g., normal force, friction, tension, spring force).

Long-range force

A force that acts through a field without contact; near Earth the main example is gravity.

Free-body diagram (FBD)

A simplified sketch showing one chosen object (or system) and all external forces acting on it; used as a “force inventory.”

External force

A force exerted on the chosen object/system by something outside it; only external forces appear on a system FBD.

Net force (ΣF)

The vector sum of all forces acting on an object; determines acceleration via Newton’s second law.

Force inventory

The complete list of all external forces on the chosen object; if incomplete/incorrect, the resulting equations will be wrong.

Newton’s First Law

If the net external force on an object is zero, its velocity remains constant (including the special case of rest).

Inertial frame

A reference frame in which objects with zero net force do not accelerate; most AP Physics problems use the lab frame as approximately inertial.

Equilibrium

A condition where the net force is zero: Σ⃗F = 0⃗, implying zero acceleration (object may be at rest or move at constant velocity).

Static equilibrium

Equilibrium with zero velocity (object is at rest and Σ⃗F = 0⃗).

Dynamic equilibrium

Equilibrium with nonzero constant velocity (moving steadily while Σ⃗F = 0⃗).

Newton’s Second Law

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

Component form of Newton’s Second Law

Applying ΣF = ma separately along chosen axes, e.g., ΣFx = max and ΣFy = may.

Coordinate axes choice (for FBDs)

Choosing axes to simplify component breakdown (often parallel/perpendicular to an incline or along acceleration).

Weight (gravitational force near Earth)

The gravitational force Earth exerts on an object near its surface: F_g = mg downward (toward Earth’s center).

Normal force (N)

A contact force exerted by a surface on an object, perpendicular to the surface; it adjusts based on constraints and other forces and is not always mg.

Tension (T)

The pulling force transmitted through a rope/string/cable; typically uniform along a massless rope over a frictionless, massless pulley.

Kinetic friction (f_k)

Friction when surfaces slide; magnitude fk = μk N and direction opposite the relative sliding motion.

Static friction (f_s)

Friction when surfaces do not slide; it adjusts as needed to prevent slipping, up to a maximum value.

Maximum static friction (f_s,max)

The largest possible static friction force before slipping begins: fs,max = μs N.

Coefficient of kinetic friction (μ_k)

A dimensionless constant in the model fk = μk N for sliding surfaces.

Coefficient of static friction (μ_s)

A dimensionless constant setting the limit for static friction: fs ≤ μs N.

Hooke’s law

Spring-force model stating spring force magnitude is proportional to displacement: F_s = kx, directed opposite the displacement (restoring).

Spring constant (k)

A measure of spring stiffness in Hooke’s law; larger k means a stiffer spring.

Displacement from equilibrium (x)

How far a spring is stretched or compressed from its natural (equilibrium) length; used in Hooke’s law F_s = kx.

Restoring force

A force (e.g., spring force) that points opposite the displacement and tends to return a system to equilibrium.

Drag / air resistance

A force from a fluid (like air) that acts opposite velocity and increases with speed; a specific model must be given to compute it quantitatively.

Terminal speed

A condition in which drag balances weight so net force is zero and speed becomes constant.

Constraint (in multi-object problems)

A relationship between motions imposed by connections (e.g., an inextensible rope), reducing the number of independent accelerations.

System approach

Analyzing multiple connected objects as one combined system so internal forces (like tension between them) cancel, leaving only external forces.

Internal force

A force between parts of a chosen multi-object system; internal forces often cancel in the system’s net-force accounting.

Atwood machine

Two masses hanging over an ideal pulley; applying Newton’s second law gives acceleration a = ((m2 − m1)g)/(m1 + m2) when m2 > m1.

Uniform tension assumption (ideal rope/pulley)

For a massless, non-stretching rope over a frictionless, massless pulley, the tension is the same throughout a single continuous rope segment.

Same-acceleration constraint (taut rope)

Under ideal assumptions, connected masses share the same acceleration magnitude along the rope (directions opposite if they move oppositely).

Centripetal acceleration (a_c)

The inward acceleration required for circular motion: a_c = v^2/r, directed toward the center of curvature.

Radial force equation (circular motion)

Newton’s second law along the inward radial direction: ΣF_radial = m(v^2/r).

“Centripetal force” (meaning)

Not a new force; it refers to the net inward (radial) force provided by real forces (tension, friction, normal, gravity).

Maximum speed on a flat curve (friction-limited)

For a car turning on level ground, the no-slip condition gives vmax = √(μs g r).

Top-of-vertical-circle tension equation

At the top of a vertical circle, inward is downward, so T + mg = m(v^2/r), hence T = m(v^2/r) − mg.

Just-taut condition (string in vertical circle)

The minimum speed at the top to keep a string taut occurs when T = 0, giving v = √(gr).

Apparent weight

What you “feel” or what a scale reads in many problems; usually equals the normal force N, which can differ from mg during acceleration.

Scale reading (in elevator problems)

The normal force exerted by the scale on the person; this is the reported “weight” on the scale, not mg.

Elevator equation for apparent weight

For a person of mass m: N − mg = ma (with sign set by the chosen vertical positive direction).

Free fall (scale reads zero)

If the person/elevator accelerates downward with a = g, then N = 0 and the scale reads zero.

Non-inertial frame

An accelerating reference frame in which Σ⃗F = m⃗a does not hold in its simple form unless pseudo-forces are added.

Pseudo-force (fictitious force)

A force introduced when analyzing motion in a non-inertial frame; magnitude ma and direction opposite the frame’s acceleration.

Newton’s Third Law

If object A exerts a force on object B, then B exerts an equal-magnitude, opposite-direction force on A; the pair acts on different objects.

Action–reaction pair identification

A valid third-law pair is the same interaction type, equal magnitude, opposite direction, simultaneous, and acting on two different objects (e.g., “force on B by A” with “force on A by B”).