AP Physics 1 Unit 2 Learning Notes: Force and Translational Dynamics

Force

An interaction that can change an object’s motion by causing acceleration; treated as a vector (magnitude and direction).

Vector (as used for forces)

A quantity with both magnitude and direction; forces must be added using vector addition.

System (in dynamics)

The object or collection of objects chosen for analysis; determines which forces are included on the free-body diagram.

External force

A force on the system due to something outside the system; these are the forces that appear on the system’s FBD.

Internal force

A force between parts inside the chosen system; does not appear on an FBD of the whole system.

Free-body diagram (FBD)

A simplified sketch showing only the forces acting on the chosen system, drawn as vectors on a dot/box representing the object.

Net force (ΣF)

The vector sum of all external forces acting on the system; not drawn as a separate force on an FBD.

Weight (W or mg)

The gravitational force exerted by Earth on an object; magnitude mg, directed downward toward Earth’s center.

Gravitational acceleration (g)

The local acceleration due to gravity (near Earth about 9.8 m/s²); affects weight but not mass.

Mass (m)

A measure of inertia (resistance to acceleration); does not depend on location (Moon vs Earth).

Normal force (F_N)

A contact force exerted by a surface on an object, perpendicular to the surface; adjusts based on the situation.

Friction force

A contact force parallel to a surface that opposes relative motion or the tendency for relative motion between surfaces.

Static friction (f_s)

Friction that acts when surfaces are not sliding; its magnitude adjusts as needed up to a maximum.

Maximum static friction (f_s,max)

The largest possible static friction force before slipping begins; fs,max = μs F_N.

Coefficient of static friction (μ_s)

Dimensionless constant for a pair of surfaces that sets the maximum static friction via μs FN.

Kinetic friction (f_k)

Friction that acts when surfaces are sliding; modeled approximately as fk = μk F_N.

Coefficient of kinetic friction (μ_k)

Dimensionless constant for sliding surfaces used in fk = μk FN; typically less than μs.

Tension (T)

A pulling force transmitted through a string/rope/cable; acts along the string and pulls away from the object.

Applied force

A push or pull exerted on an object by a person or another object (not one of the named standard forces like weight).

Spring force

A force exerted by a spring, typically modeled by Hooke’s law in later units; acts to restore the spring toward equilibrium length.

Newton’s first law

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

Inertia

The tendency of an object to resist changes in its motion; quantified by mass in Newton’s second law.

Inertial reference frame

A non-accelerating frame in which Newton’s laws apply in their simplest form (AP problems usually treat the ground as inertial).

Equilibrium

A condition with zero acceleration, so the net force is zero (ΣF = 0).

Static equilibrium

Equilibrium where the object’s velocity is zero and remains zero.

Dynamic equilibrium

Equilibrium where the object moves with constant velocity (nonzero allowed) and has zero acceleration.

Newton’s second law

The relationship between net external force, mass, and acceleration: ΣF = ma (vector form).

Component form of Newton’s second law

Writing Newton’s second law separately along axes, typically ΣFx = max and ΣFy = may.

Newton (N)

SI unit of force; 1 N = 1 kg·m/s² (the force needed to accelerate 1 kg at 1 m/s²).

Force components

The parts of a vector along chosen axes; used to simplify equations when forces are at angles.

Resolve a force into components

Expressing a force vector as perpendicular components, e.g., Fx = F cosθ and Fy = F sinθ (with θ from +x).

Incline coordinate choice

A common axis choice on ramps: x parallel to the incline and y perpendicular to the incline to simplify component equations.

Parallel weight component on an incline (mg sinθ)

The component of weight along the slope (down the incline) when θ is the incline angle from horizontal.

Perpendicular weight component on an incline (mg cosθ)

The component of weight into the surface (perpendicular to the incline) when θ is the incline angle from horizontal.

Sine/cosine incline check

Reasoning tool: for small incline angles, the parallel component must be small, so it corresponds to mg sinθ (not mg cosθ).

Apparent weight

What a scale reads; typically the normal force the scale exerts on you, which can differ from mg in acceleration situations.

Elevator apparent weight relation

For upward-positive: FN − mg = ma, so FN = m(g + a) when accelerating upward and F_N = m(g − |a|) when accelerating downward.

Normal force on a frictionless incline

With no perpendicular acceleration, the normal force equals the perpendicular weight component: F_N = mg cosθ.

Friction direction rule

Friction points opposite relative motion (kinetic) or opposite the direction the object would start moving without friction (static).

“Motion implies force” misconception

Incorrect idea that moving objects must have a force in the direction of motion; actually forces cause acceleration, not velocity.

Ideal string assumption

String is massless and does not stretch, so connected objects share acceleration constraints and tension is uniform (in the ideal model).

Ideal pulley assumption

Pulley is massless and frictionless, so tension is the same on both sides in standard AP setups.

Acceleration constraint (taut string)

Connected masses on a taut, non-stretching string have the same acceleration magnitude along the string.

Atwood machine

Two hanging masses connected by a massless string over a frictionless pulley; acceleration depends on the mass difference.

Atwood acceleration (ideal)

For m2 > m1, a = ((m2 − m1)g)/(m1 + m2).

System approach (connected objects)

Treating multiple objects as one system to find acceleration; internal forces (like tension/contact) cancel for the combined system.

Object-by-object approach (connected objects)

Writing ΣF = ma for each object separately and solving simultaneously for shared unknowns like tension and acceleration.

Newton’s third law

Forces come in equal-and-opposite pairs acting on different objects: if A exerts a force on B, B exerts an equal and opposite force on A.

Third-law pair properties

A third-law pair acts on two different objects, has equal magnitude and opposite direction, and is the same type of force.

Angled pull effect on normal force

For a pull F at angle θ above horizontal with no vertical acceleration: FN = mg − F sinθ, reducing friction because friction depends on FN.