Introduction to the Laws of Motion
Welcome to one of the most fundamental parts of physics! In Unit 2, we are exploring Translational Dynamics, which is just a fancy way of saying "why things move." While Kinematics (Unit 1) described motion, Newton's Laws explain the causes of that motion. In this chapter, we focus on Newton's First Law and Newton's Third Law. These laws provide the "rules of the game" for how objects interact and how they resist changes to their state of being. Don't worry if these concepts feel a bit abstract at first—once you see the patterns, they become second nature!
Newton’s First Law: The Law of Inertia
Newton’s First Law states that an object at rest will stay at rest, and an object in motion will stay in motion with a constant velocity (same speed and same direction) unless acted upon by a net external force.
What is Inertia?
Inertia is not a force. Instead, it is a property of matter. It is the natural tendency of an object to resist any change in its motion.
• If an object is sitting still, its inertia makes it want to stay sitting still.
• If an object is sliding at \(5 \text{ m/s}\) to the right, its inertia makes it want to keep sliding at \(5 \text{ m/s}\) to the right forever.
Mass is the quantitative measure of inertia. The more mass an object has, the more it resists changing its motion. It is much harder to stop a moving bowling ball than a moving tennis ball because the bowling ball has more mass (and therefore more inertia).
The Concept of Equilibrium
When the sum of all forces acting on an object is zero, we say the object is in translational equilibrium. This is written mathematically as:
\( \sum \vec{F} = 0 \)
According to the First Law, if \( \sum \vec{F} = 0 \), the object’s acceleration must be zero (\( \vec{a} = 0 \)). This leads to two possible states:
1. Static Equilibrium: The object is at rest (\( \vec{v} = 0 \)).
2. Dynamic Equilibrium: The object is moving at a constant velocity (\( \vec{v} = \text{constant} \)).
Inertial Reference Frames
Newton’s laws only work in what we call Inertial Reference Frames. These are frames of reference that are not accelerating. For the AP Physics 1 exam, you should assume the frame of reference is inertial unless the problem specifically tells you otherwise.
Quick Review: If you see a car moving at a constant speed in a straight line, the net force on it is zero! Many students mistakenly think a force is needed to keep an object moving. In reality, a force is only needed to change the motion.
Newton’s Third Law: Interaction Pairs
Newton’s Third Law is often quoted as "for every action, there is an equal and opposite reaction," but in AP Physics, we need to be more precise. It describes how two objects interact with each other.
The Law of Interaction
Whenever object A exerts a force on object B, object B simultaneously exerts a force on object A that is equal in magnitude and opposite in direction.
In vector notation, this looks like:
\( \vec{F}_{A \text{ on } B} = -\vec{F}_{B \text{ on } A} \)
Key Characteristics of Third-Law Pairs
To identify a true Newton's Third Law pair (also called an interaction pair), look for these three things:
1. Same Magnitude: The forces are exactly the same size.
2. Opposite Direction: They point in exactly opposite directions.
3. Different Objects: This is the most important rule! The two forces must act on two different objects. Because they act on different objects, interaction pairs never cancel each other out on a single free-body diagram.
Real-World Example: Walking
When you walk, your foot pushes backward on the ground (\( \vec{F}_{\text{foot on ground}} \)). According to the Third Law, the ground pushes forward on your foot with an equal force (\( \vec{F}_{\text{ground on foot}} \)). It is this forward force from the ground that actually moves you forward!
Did you know? This law applies even to gravity. If the Earth pulls down on you with a gravitational force of \( 700 \text{ N} \), you are actually pulling up on the Earth with a gravitational force of \( 700 \text{ N} \). You move more than the Earth because the Earth has significantly more inertia (mass)!
Common Pitfalls to Avoid
The "Normal Force vs. Gravity" Trap
One of the most common mistakes in physics is thinking that the Normal Force (\( \vec{F}_n \)) and the Force of Gravity (\( \vec{F}_g \)) acting on a book sitting on a table are a Third Law pair.
Why they are NOT a pair:
• Both forces are acting on the same object (the book).
• Third Law pairs must involve two objects.
• The actual pair for the book's weight (\( \vec{F}_{\text{Earth on book}} \)) is the force of the book pulling up on the Earth (\( \vec{F}_{\text{book on Earth}} \)).
• The actual pair for the normal force (\( \vec{F}_{\text{table on book}} \)) is the force of the book pushing down on the table (\( \vec{F}_{\text{book on table}} \)).
Forces and Free-Body Diagrams (FBDs)
When you draw a Free-Body Diagram (as introduced in Chapter 2.2), you only draw the forces acting on the object. You should never draw both halves of a Newton’s Third Law pair on the same FBD. If you are drawing an FBD for a block, you only draw the forces the environment exerts on that block.
Summary of Key Takeaways
• Newton’s First Law defines inertia. Objects will keep their current velocity (including zero) unless a net external force forces them to change.
• Inertia is measured by mass. More mass = more resistance to change.
• Equilibrium (\( \sum \vec{F} = 0 \)) means there is no acceleration. This applies to objects at rest or objects moving at a constant velocity.
• Newton’s Third Law explains that forces always come in pairs. If A pushes B, B pushes A back just as hard in the opposite direction.
• Interaction pairs always act on different objects and therefore cannot cancel each other out on a single object's FBD.
Next Chapter Preview: Now that we understand what happens when forces are balanced (First Law) and how objects interact (Third Law), we will move on to Newton's Second Law (\( \sum \vec{F} = m\vec{a} \)) to calculate exactly how much an object will accelerate when forces are unbalanced!