Fundamental Laws of Motion to Know for AP Physics C: Mechanics (AP)

The Fundamental Laws of Motion, established by Sir Isaac Newton, form the cornerstone of classical mechanics and are essential for understanding motion and forces in AP Physics C: Mechanics. These three laws describe how objects move, how forces cause acceleration, and how every action is met with an equal and opposite reaction. Mastering these principles allows students to analyze real-world scenarios, solve complex problems, and connect physics concepts to the behavior of objects in motion.

1. Newton’s Laws of Motion

Sir Isaac Newton’s three laws of motion are the foundation of classical mechanics. Understanding these laws is essential for solving problems in AP Physics C: Mechanics.

a. Newton's First Law: Law of Inertia

• States that an object remains at rest or in uniform motion (constant velocity) unless acted upon by a net external force.

• Inertia, as described by Newton's First Law of Motion, is the natural tendency of an object to resist changes in its state of motion or rest. This means that an object at rest will remain at rest, and an object in motion will continue moving at a constant velocity in a straight line unless acted upon by an external force. The amount of inertia an object has is directly proportional to its mass; objects with greater mass require more force to change their motion.

• The greater the mass, the greater the inertia.

Equation:

No specific formula, but implies Fnet = 0 when no acceleration occurs.

Application:

• Objects on a frictionless surface remain in motion.

• A book on a table remains at rest unless pushed.

b. Newton's Second Law: Force and Acceleration

• Newton's second law can be formally stated as the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

• The law explains that a greater force results in a greater acceleration for a given mass, while a larger mass requires a greater force to achieve the same acceleration. This principle provides a quantitative description of how forces affect the motion of objects

Equation:

Fnet​ = ma

Where:

• Fnet​ - Net force (in Newtons, N)

• m - Mass of the object (in kilograms, kg)

• a - Acceleration of the object (in m/s^2)

Key Concepts:

• Acceleration (a) - is directly proportional to the net force (Fnet​) and inversely proportional to the mass (m).

• Fnet​ - is a vector, so both magnitude and direction are important.

Application:

• Calculating acceleration from a known force and mass.

• Free-body diagrams to identify net forces.

Derived Forms:

• a = Fnet/m​​

• Fnet,x = max​, Fnet,y = may (for components).

c. Newton's Third Law: Action and Reaction

• Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on a second object, the second object simultaneously exerts a force of the same magnitude but in the opposite direction on the first object.

• These forces act on different objects and occur as a pair, ensuring that they do not cancel each other out. This principle explains interactions such as the push of a swimmer's hands against water propelling them forward or the recoil of a gun when it fires a bullet.

• The law highlights the symmetry and mutuality of forces in any physical interaction.

Equation:

No explicit formula, but expressed as: Faction ​= −Freaction​

Where:

• Forces are equal in magnitude and opposite in direction.

Key Concepts:

• Forces always occur in pairs, acting on two different objects.

• Action-reaction forces do not cancel each other because they act on different bodies.

Applications:

• A rocket pushes exhaust gases downward; the gases push the rocket upward.

• A swimmer pushes water backward, and the water pushes the swimmer forward.

2. Conservation of Linear Momentum

• The principle of conservation of linear momentum states that the total momentum of a closed system remains constant unless acted upon by an external force.

• Momentum is a vector quantity, calculated by multiplying an object's mass by its velocity. This concept is fundamental in analyzing interactions like collisions, where the total momentum before and after the event remains unchanged if no external forces are involved.

3. Work-Energy Theorem

• The work-energy theorem asserts that the work done on an object is equal to the change in its kinetic energy.

• This principle connects the concept of work (force applied over a distance) with changes in the energy of an object’s motion. It emphasizes that work can transfer energy into or out of a system, affecting how the object's velocity or motion changes.

4. Conservation of Energy

• The conservation of energy principle states that energy cannot be created or destroyed but can only be transformed from one form to another. In an isolated system, the total energy remains constant, though it may change forms, such as from kinetic energy to potential energy.

• This law underpins various physical phenomena and helps explain processes in mechanics, thermodynamics, and other fields.

5. Principle of Conservation of Angular Momentum

• The conservation of angular momentum states that if no external torque acts on a system, its total angular momentum remains constant. Angular momentum is the rotational equivalent of linear momentum and depends on the object’s mass distribution and rotational velocity. 

• This principle is key in understanding rotational dynamics, such as the motion of spinning objects or celestial bodies.

6. Kepler's Laws of Planetary Motion:

• Kepler's laws describe the motion of planets around the Sun: the first law states that planets orbit in ellipses with the Sun at one focus, the second law says a planet sweeps out equal areas in equal times, and the third law relates the square of a planet's orbital period to the cube of its average distance from the Sun. 

• These laws laid the foundation for understanding planetary motion and gravitation. They highlight the elliptical nature of orbits and the relationship between distance and orbital speed.

7. Hooke's Law for Springs

• Hooke's Law describes the force exerted by a spring as directly proportional to its displacement from the equilibrium position, expressed mathematically as F = -kx, where k is the spring constant

• This law is fundamental in studying elastic materials and oscillatory motion, such as in springs or pendulums. It reflects the restoring force of a spring that works to return the spring to its original shape after being stretched or compressed.

8. Additional Concepts Related to Newton’s Laws

a. Force

• Is defined as any interaction that can cause a change in the motion of an object. It is a vector quantity, meaning it has both magnitude and direction, and is measured in newtons (N).

• Types of Forces:

• Gravitational Force (Fg​): Fg = mg, where g=9.8m/s2.

• Normal Force (FN​): Perpendicular to the surface of contact.

• Frictional Force (f): Opposes motion.

  • Static: fs ≤ μsFN.

  • Kinetic: fk = μkFN​.

• Tension Force (T): Force in a string, rope, or cable.

• Applied Force (Fapp): External force applied to an object.

b. Weight and Mass

• Mass (m): Amount of matter in an object (scalar).

• Weight (Fg​): Force due to gravity on an object (vector).

• Fg=mg.

c. Friction

• Static Friction (fs​): Prevents motion. fs ≤ μsFN​.

• Kinetic Friction (fk): Opposes sliding motion. fk = μkFN​.

d. Free Body Diagram (FBD)

• Is a visual representation used to show all the external forces acting on a specific object or system. It simplifies complex interactions by isolating the object in question and illustrating forces such as gravity, friction, tension, normal force, applied forces, and others, with arrows indicating both the direction and relative magnitude of each force.

• These diagrams are crucial for analyzing the object's motion or equilibrium, as they help apply Newton's Laws of Motion to determine how the forces balance or cause acceleration. By isolating the object from its surroundings, free-body diagrams provide a clear and systematic way to solve problems involving force interactions.

e. Equilibrium

• Refers to a state in which the net force and net torque acting on an object are both zero, resulting in no acceleration or rotation. There are two types of equilibrium: static equilibrium, where an object is at rest and remains stationary, and dynamic equilibrium, where an object is moving with constant velocity in a straight line.

• For an object to be in equilibrium, the vector sum of all the forces acting on it must be zero, and the sum of all torques must also be zero. This means that the forces and moments acting on the object perfectly balance each other, ensuring no change in motion or rotational state.