AP Physics – Newton’s Three Laws of Motion (Inertia, F=ma, Action-Reaction)

AP Physics – Newton’s Three Laws of Motion (Inertia, F=ma, Action?Reaction)

AP Physics: Newton’s Three Laws of Motion – Exam-Ready Study Guide

What This Is

Newton’s Three Laws of Motion are the foundation of classical mechanics—they explain how and why objects move (or don’t move). These laws appear everywhere on the AP Physics exam, from multiple-choice questions to full free-response problems (FRQs). They’re essential for understanding forces, acceleration, and interactions between objects. Real-world example: When a car suddenly stops, your body lurches forward because of inertia (Newton’s 1st Law). The seatbelt applies a force to stop you (2nd Law), and your body pushes back on the seatbelt with equal force (3rd Law).

Key Terms & Concepts

• Newton’s First Law (Law of Inertia): "An object at rest stays at rest, and an object in motion stays in motion at a constant speed in a straight line unless acted upon by an unbalanced external force."
• Inertia: An object’s resistance to changes in motion. More mass = more inertia.

• Equilibrium: When net force = 0 (object is at rest or moving at constant velocity).

• Newton’s Second Law (F = ma): "The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass."

• F = ma (Force = mass × acceleration)
  • F = net force (N, Newtons)
  • m = mass (kg)
  • a = acceleration (m/s²)

• Key idea: Force causes acceleration, not motion. A net force is needed to change velocity.

• Newton’s Third Law (Action-Reaction): "For every action, there is an equal and opposite reaction."

• Forces always come in pairs (e.g., you push on a wall, the wall pushes back on you).

• Important: The two forces act on different objects (so they don’t cancel out).

• Free-Body Diagram (FBD): A sketch showing all forces acting on a single object (e.g., gravity, normal force, friction, tension).

• Rules:

  • Draw forces as arrows pointing away from the object.
  • Label each force (e.g., F? for gravity, F? for normal force).
  • Only include forces acting on the object, not forces the object exerts on others.

• Net Force (?F): The vector sum of all forces acting on an object.

• If ?F = 0-object is in equilibrium (no acceleration).

• If ?F-0-object accelerates in the direction of the net force.

• Weight (F?): The force of gravity on an object: F? = mg (where g = 9.8 m/s² on Earth).

• Weight-mass! Mass is constant; weight changes with gravity (e.g., you weigh less on the Moon).

• Normal Force (F?): The perpendicular force a surface exerts to support an object.

• Not always equal to weight! (e.g., on an incline or in an elevator accelerating upward).

• Tension (F?): The pulling force exerted by a rope, string, or cable.

• Assumption: Massless, unstretchable ropes-tension is the same throughout.

• Friction (F_f): A force that opposes motion between two surfaces in contact.

• Static friction (F?): Prevents motion (max value = F?).
• Kinetic friction (F?): Acts on moving objects (F? = F?).
• ? (mu): Coefficient of friction (unitless, depends on materials).

Step-by-Step: Solving Newton’s Laws Problems

Follow this exam-proof method for any force problem:

1. Draw a Free-Body Diagram (FBD):
2. Isolate the object of interest.
3. Sketch all forces acting on it (gravity, normal, friction, tension, applied forces).

4. Label forces with variables (e.g., F?, F?, F?).

5. Choose a Coordinate System:

6. Align axes with the direction of acceleration (e.g., along an incline).

7. Break forces into x and y components if needed (e.g., F? on an incline = mg sin?).

8. Write Newton’s Second Law Equations:

9. For each direction (x and y), write ?F = ma.

10. Example:

    • x-direction: F? - F_f = ma
    • y-direction: F? - F? = 0 (if no vertical acceleration)

11. Solve for Unknowns:

12. Use algebra to solve for the unknown (e.g., acceleration, tension, mass).

13. Pro tip: If stuck, check if you missed a force (e.g., friction, normal force).

14. Check Units & Reasonableness:

15. Ensure all forces are in Newtons (N) and accelerations in m/s².
16. Ask: Does the answer make sense? (e.g., acceleration shouldn’t be faster than a jet plane unless given extreme forces.)

Common Mistakes

• Mistake: Forgetting that F = ma requires net force, not just any force.

• Correction: Always sum all forces first (?F) before plugging into F = ma.

• Mistake: Assuming the normal force always equals weight.

• Correction: F? = mg only on a flat surface with no vertical acceleration. On an incline or in an accelerating elevator, F?-mg.

• Mistake: Mixing up action-reaction pairs (e.g., thinking they cancel out).

• Correction: Action-reaction forces act on different objects, so they don’t cancel. Example: Earth pulls you down (gravity), you pull Earth up (but Earth’s mass is huge, so its acceleration is negligible).

• Mistake: Ignoring friction when it’s present.

• Correction: Always check if the problem mentions a surface (e.g., "rough floor" = friction is involved).

• Mistake: Using F = ma for circular motion (e.g., centripetal force).

• Correction: For circular motion, use F = mv²/r (centripetal force). F = ma still applies, but a is centripetal acceleration.

AP Exam Insights

• What’s Frequently Tested?
• Free-body diagrams (FBDs): You’ll draw these in every FRQ involving forces.
• Inclined planes: Expect problems where you must break F? into components (mg sin? and mg cos?).
• Elevator problems: Accelerating upward/downward changes the normal force (e.g., F? = m(g + a) when accelerating up).

• Third Law pairs: Multiple-choice questions love asking which forces are action-reaction pairs (e.g., "Is the normal force the reaction to gravity?" No! They act on the same object.)

• Tricky Distinctions:

• Mass vs. Weight: Mass is constant; weight depends on gravity.
• Static vs. Kinetic Friction: Static friction matches applied force up to a max; kinetic friction is constant.

• Net Force vs. Individual Forces: A net force causes acceleration, but individual forces (like tension) can be larger than the net force.

• FRQ Tips:

• Always show your FBD—graders give points for it!
• Label forces clearly (e.g., F? for tension, not just "T").
• Write ?F = ma for each direction (x and y), even if one direction has no acceleration.

Quick Check Questions

1. Multiple Choice

A 5 kg block is pushed with a 20 N force on a frictionless surface. What is its acceleration? (A) 0.25 m/s² (B) 4 m/s² (C) 100 m/s² (D) 5 m/s²

Answer: (B) 4 m/s² Explanation: Use F = ma-a = F/m = 20 N / 5 kg = 4 m/s².

2. Free-Response (Short)

A 10 kg box rests on a horizontal surface. A 30 N horizontal force is applied, but the box does not move. (a) Draw a free-body diagram for the box. (b) What is the magnitude of the static friction force acting on the box?

Answer: (a) FBD should show: - Downward arrow: F? = mg = 98 N - Upward arrow: F? = 98 N - Right arrow: F_applied = 30 N - Left arrow: F_f (static) = 30 N

(b) 30 N (since the box isn’t moving, static friction balances the applied force).

3. Multiple Choice

A book rests on a table. Which of the following is an action-reaction pair according to Newton’s Third Law? (A) The weight of the book and the normal force from the table. (B) The force of the book on the table and the force of the table on the book. (C) The weight of the book and the force of the Earth on the book. (D) The normal force from the table and the force of the Earth on the table.

Answer: (B) Explanation: Action-reaction pairs act on different objects (book on table, table on book). (A) and (C) act on the same object, and (D) is unrelated.

Last-Minute Cram Sheet

1. Newton’s 1st Law: Objects resist changes in motion (inertia). No net force = no acceleration.
2. F = ma: Net force causes acceleration. F must be the net force, not just one force.
3. Newton’s 3rd Law: Forces come in pairs (equal and opposite, on different objects).
4. Weight = mg (g = 9.8 m/s² on Earth). Weight-mass!
5. Normal force (F?)-weight unless on a flat surface with no vertical acceleration.
6. Static friction-F?, kinetic friction = F?.
7. Always draw a free-body diagram (FBD) for force problems.
8. Break forces into x and y components (e.g., on an incline: mg sin? and mg cos?).
9. ?F = ma in each direction (x and y).
10. Action-reaction pairs act on different objects—they don’t cancel! Common trap in multiple-choice.