Rucete ✏ AP Physics C In a Nutshell
3. Newton’s Laws
This chapter introduces Newton’s three laws of motion, the distinction between mass and weight, and various applications of Newton’s laws including static equilibrium, friction, tension, and circular motion problems.
Newton’s First Law (Law of Inertia)
• An object at rest stays at rest, and an object in motion stays in motion at constant velocity unless acted on by a net external force.
• Net force: the vector sum of all forces acting on an object.
• Inertia: resistance to changes in motion, measured by mass.
• Newton’s laws apply only in inertial reference frames (frames moving at constant velocity).
Newton’s Second Law
• The net force on an object equals its mass times its acceleration:
Fnet = ma
• Force and acceleration are vectors pointing in the same direction.
• SI unit of force: newton (N), where 1 N = 1 kg·m/s².
Newton’s Third Law
• For every force exerted by object A on object B, object B exerts an equal and opposite force on object A.
• Forces always occur in pairs, acting on different objects.
Mass vs. Weight
• Mass: measure of an object’s inertia, remains constant everywhere.
• Weight: gravitational force on an object; w = mg
• Weight varies with gravitational field strength, but mass does not.
Types of Forces
Gravitational Force
• Weight = mg, always directed toward the center of Earth.
Normal Force
• Perpendicular contact force exerted by a surface.
• On flat surfaces: N = mg if no vertical acceleration.
• On inclined planes: N = mg·cos(θ).
Frictional Force
• Opposes relative motion between surfaces.
• Static friction: prevents motion, up to maximum fs,max = μsN.
• Kinetic friction: fk = μkN (after motion starts).
• Typically, μs > μk.
Tension
• Force transmitted through a rope, string, or cable.
• Tension is the same throughout an ideal (massless, non-stretching) rope.
General Approach to Solving Newton’s Law Problems
• Draw a free-body diagram (FBD) labeling all forces clearly.
• Choose a convenient coordinate system (e.g., align axes with inclined planes).
• Break forces into components along chosen axes.
• Apply Newton’s Second Law separately in x- and y-directions.
• Solve for unknowns like acceleration, tension, normal force, or friction.
Common Applications
Inclined Planes
• Gravity components: Parallel = mg·sin(θ), Perpendicular = mg·cos(θ).
Atwood Machines
• Two masses connected by a rope over a pulley.
• Analyze each mass separately, but tension links them.
• Common acceleration for both masses.
Elevators
• Apparent weight changes if elevator accelerates up or down.
• N = m(g ± a) (plus for accelerating upward, minus for downward).
Banked Curves
• Banking helps provide centripetal force without relying solely on friction.
• Ideal speed for no friction: v = √(rg·tan(θ)).
In a Nutshell
Newton’s laws form the core of mechanics, relating forces to changes in motion. Solving problems requires systematic free-body diagrams, careful vector resolution, and applying F = ma in chosen directions. Mastery of these techniques allows prediction and explanation of motions from sliding blocks to orbiting planets.