AP Physics 1 Unit 2 Notes: Understanding Motion Through Forces and Systems

System (in mechanics)

A chosen collection of objects analyzed together; the system boundary determines which forces are internal vs. external and can simplify applying Newton’s laws.

System boundary

The (conceptual) dividing line that separates the objects included in a system from everything outside; it determines whether a force is labeled internal or external.

Internal force

A force between objects that are both inside the chosen system; internal forces often come in Newton’s third-law pairs and do not appear in the net external force on the system.

External force

A force exerted on the system by an object outside the system boundary; external forces determine the acceleration of the system’s center of mass.

Center of mass (COM)

The mass-weighted average position of a system; the point that moves as if all the system’s mass were concentrated there for translational motion.

Center of mass (1D) formula

For point masses on a line: xcm = (Σ mi xi)/(Σ mi).

Center of mass (2D) formulas

For point masses in a plane: xcm = (Σ mi xi)/(Σ mi) and ycm = (Σ mi yi)/(Σ mi).

Total mass (M) of a system

The sum of all masses in the system (M = Σ mi); used in the system-level equation ΣFext = M a_cm.

System-level Newton’s second law (COM form)

ΣFext = M acm; the center of mass accelerates according to the net external force on the system.

Zero net external force on a system

If ΣFext = 0, then acm = 0, meaning the center of mass moves with constant velocity (possibly at rest).

Free-body diagram (FBD)

A simplified sketch showing all external forces acting on a chosen object or system; it defines what forces go into Newton’s second law for that choice.

Isolate the object/system (FBD step)

In making an FBD, you mentally separate the chosen object/system from its surroundings so you can include only forces acting on it.

Interaction (source of forces)

A contact or non-contact relationship between objects that produces forces; forces exist only due to interactions (e.g., gravity, normal contact, tension).

Weight (gravitational force near Earth)

The force Earth exerts on a mass: F_g = mg, directed downward toward Earth’s center.

Normal force (N)

The contact force a surface exerts on an object, perpendicular to the surface; it adjusts to satisfy Newton’s laws and is not always equal to mg.

Tension (T)

The pulling force exerted by a string/rope, directed along the string away from the object it acts on.

Friction force (f)

A contact force parallel to the surface that opposes relative motion (or impending relative motion) between surfaces.

Static friction (f_s)

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

Kinetic friction (f_k)

Friction during slipping; its magnitude is fk = μk N and it opposes the direction of relative motion.

Hooke’s law (spring force magnitude)

For an ideal spring, the restoring force magnitude is F_s = kx, directed opposite the displacement from equilibrium.

Newton’s first law

If the net force on an object is zero, it maintains constant velocity (including staying at rest): ΣF = 0 ⇒ a = 0.

Inertia

The tendency of an object to resist changes in velocity; mass is the quantitative measure of inertia.

Translational equilibrium

A condition where the net force is zero so acceleration is zero; typically written as ΣFx = 0 and ΣFy = 0.

Newton’s third law

When two objects interact, they exert equal-magnitude, opposite-direction forces on each other: F{A→B} = −F{B→A}; the pair acts on different objects.

Newton’s second law

The net external force on an object equals its mass times its acceleration: ΣF = ma, where ΣF is the vector sum of external forces.