Newton's First Law
Why this matters
Have you ever been on a long road trip, driving down a straight highway? You set the cruise control to 65 mph and for miles, the car just... goes. Your foot is off the gas pedal, but the car doesn't slow down, and it doesn't speed up. It just maintains that perfect 65 mph.
You might think, "The engine is pushing the car forward, so there must be a forward force." And you're right! But what about air resistance pushing back on the car? And friction in the tires? Those are forces, too.
The magic of cruise control is that the engine adjusts its push to be exactly equal and opposite to all the forces trying to slow you down. All the forces cancel out. This state of balanced forces is the key to Newton's First Law, and it explains why things can be moving without speeding up or slowing down. We'll explore both sides of this law: objects staying still and objects moving steadily.
Diagram
Concept map
flowchart TD
A[Start: Analyze forces on an object] --> B{Is the net force zero? (ΣF = 0)};
B -- Yes --> C{Is the object's initial velocity zero?};
B -- No --> D[Object accelerates (a ≠ 0) --- Newton's 2nd Law];
C -- Yes --> E[Object remains at rest (Static Equilibrium)];
C -- No --> F[Object continues at constant velocity (Dynamic Equilibrium)];
Core explanation
Let's break down one of the most fundamental ideas in all of physics. It might seem simple at first, but it has some subtleties that are really important to master for the AP exam.
What is "Net Force"?
Imagine a game of tug-of-war. Team A pulls to the left with 100 pounds of force. Team B pulls to the right with 100 pounds of force. What happens to the rope? Nothing. It stays put. The forces are balanced.
Now, what if Team B brings in their friend Marcus, and they now pull to the right with 120 pounds of force? The rope will start moving to the right. The forces are unbalanced.
The net force is the overall, total force on an object after you add up all the individual forces, considering their directions. It's the vector sum of all forces. We write this as:
ΣF⃗ = F⃗₁ + F⃗₂ + F⃗₃ + ...
The Greek letter Sigma (Σ) just means "sum of." So, ΣF⃗ means "the sum of all force vectors." In our first tug-of-war game, the net force was zero. In the second game, it was 20 pounds to the right.
Translational Equilibrium: The State of Balance
When the net force on an object is zero, we say the object is in translational equilibrium.
ΣF⃗ = 0
This is the mathematical condition for Newton's First Law. "Translational" just refers to motion where the object moves from one point to another without rotating. "Equilibrium" means balance. So, it's a balance of forces that affects straight-line motion.
Newton's First Law: The Law of Inertia
Here's the law itself:
An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by a nonzero net force.
In simpler terms: If ΣF⃗ = 0, then the object's velocity v⃗ is constant.
This is where we need to be very careful. "Constant velocity" has two important meanings:
- The object is at rest (
v⃗ = 0). - The object is moving at a constant speed in a straight line (
v⃗ = constant ≠ 0).
Case 1: Static Equilibrium (At Rest) This is the intuitive one. A book sitting on your desk. Gravity pulls it down. The desk pushes it up with an equal and opposite normal force. The net force is zero, so the book just sits there. Its velocity is constant (at zero).
Case 2: Dynamic Equilibrium (Constant Velocity) This is where most students get stuck. They think that if an object is moving, there must be a net force causing the motion. This is the biggest misconception in early physics.
A net force doesn't cause velocity. A net force causes a change in velocity (acceleration).
Think back to the car on cruise control. The engine provides a forward push (applied force). Air resistance and friction provide a backward drag (resistive forces). At 65 mph, these forces are perfectly balanced. ΣF⃗ = 0. Because the net force is zero, the velocity doesn't change. It stays at a constant 65 mph. If you wanted to speed up to 70 mph (i.e., accelerate), you'd need to hit the gas, making the engine's force greater than the drag, creating a nonzero net force.
Forces are Independent in Different Dimensions
Forces are vectors, which means they have direction. We can analyze the forces in the horizontal (x) and vertical (y) dimensions separately. An object can be in equilibrium in one dimension but not the other.
Imagine sliding a puck across a perfectly frictionless air hockey table.
- Vertical (y-direction)The force of gravity pulls the puck down. The table pushes it up with a normal force. These are balanced.
ΣF_y = 0. The puck isn't flying up into the air or crashing through the table. - Horizontal (x-direction)Once you push it, there are no horizontal forces (we said it's frictionless!). So,
ΣF_x = 0.
Because the net force is zero in both dimensions, the puck will glide at a constant velocity forever (or until it hits a wall). Its vertical velocity stays zero, and its horizontal velocity stays constant.
What's an Inertial Reference Frame?
This is a slightly more advanced idea, but it's the foundation for all of Newton's laws. An inertial reference frame is a point of view (a coordinate system) that is not accelerating.
Imagine you're on a smoothly moving train. If you toss a ball in the air, it goes up and comes straight back down into your hand, just like it would if you were standing on the ground. The train (and the ground) are inertial reference frames. Newton's First Law works perfectly.
Now, imagine the train suddenly lurches forward. If you toss the ball up, it will seem to fly backward relative to you. From your perspective, it accelerated backward without any horizontal force acting on it! This violates Newton's First Law. That's because you are in a non-inertial (accelerating) reference frame.
For AP Physics 1, you can almost always assume you are working in an inertial reference frame, like a lab on Earth. The key takeaway is that Newton's laws only hold true from a non-accelerating viewpoint.
Worked examples
Let's apply these concepts to a couple of classic AP-style problems.
A Hanging Traffic Light (Static Equilibrium)
Problem: A 12 kg traffic light is suspended by two cables as shown. Cable 1 makes a 30° angle with the horizontal, and Cable 2 makes a 45° angle. Find the tension in each cable. (Use g = 9.8 m/s²)
Solution Walkthrough:
- 1Identify the GoalWe need to find the magnitudes of the tension forces,
T₁andT₂. - 2Analyze the StateThe traffic light is "suspended," meaning it's at rest. It is in static equilibrium. This is our key insight! It tells us the net force is zero:
ΣF⃗ = 0. - 3Break it DownSince the net force is zero, the net force in the x-direction must be zero (
ΣF_x = 0), and the net force in the y-direction must be zero (ΣF_y = 0). - 4Draw a Free-Body Diagram (FBD)Draw a dot for the light. Draw three forces acting on it:
- Weight (
w⃗) pointing straight down. - Tension 1 (
T⃗₁) pointing up and to the left at 30°. - Tension 2 (
T⃗₂) pointing up and to the right at 45°.
- Weight (
- 5Set up EquationsWe need to resolve
T₁andT₂into their x and y components.T₁x = -T₁cos(30°)(negative because it points left)T₁y = +T₁sin(30°)T₂x = +T₂cos(45°)T₂y = +T₂sin(45°)- The weight is
w = mg = (12 kg)(9.8 m/s²) = 117.6 N. It's all in the y-direction.
- 6Apply Equilibrium Conditions
- ΣF_x = 0
T₂cos(45°) - T₁cos(30°) = 0T₂cos(45°) = T₁cos(30°) - ΣF_y = 0
T₁sin(30°) + T₂sin(45°) - w = 0T₁sin(30°) + T₂sin(45°) = 117.6 N
- ΣF_x = 0
- 7Solve the System of EquationsThis is now an algebra problem. From the x-equation, we can express
T₂in terms ofT₁:T₂ = T₁ * (cos(30°)/cos(45°)) ≈ T₁ * (0.866 / 0.707) ≈ 1.225 * T₁Now, substitute this into the y-equation:
T₁sin(30°) + (1.225 * T₁)sin(45°) = 117.6T₁(0.5) + (1.225 * T₁)(0.707) = 117.60.5 * T₁ + 0.866 * T₁ = 117.61.366 * T₁ = 117.6T₁ ≈ 86.1 NFinally, find
T₂:T₂ ≈ 1.225 * (86.1 N) ≈ 105.5 N
Why this matters: This problem shows how to use the fact that ΣF=0 in both dimensions to solve for unknown forces. The most common mistake is forgetting to break the tension forces into components.
Pushing a Crate (Dynamic Equilibrium)
Problem: Aaliyah pushes a 40 kg crate across a floor at a constant velocity of 1.5 m/s. She pushes with a force of 150 N. What is the force of kinetic friction (fₖ)?
Solution Walkthrough:
- 1Identify the GoalFind the force of kinetic friction,
fₖ. - 2Analyze the StateThe key phrase is "constant velocity." This immediately tells you the crate is in dynamic equilibrium. The net force is zero:
ΣF⃗ = 0. - 3Focus on the Relevant DimensionFriction is a horizontal force. Aaliyah's push is also horizontal. So let's analyze the x-direction.
- 4Apply EquilibriumSince the net force is zero overall, it must be zero in the horizontal direction:
ΣF_x = 0. - 5Set up the EquationThe forces in the x-direction are the applied push (
F_push) and the kinetic friction (fₖ), which opposes the motion.ΣF_x = F_push - fₖ = 0F_push = fₖ - 6SolveWe are given that
F_push = 150 N. Therefore,fₖ = 150 N.
Where students slip up: Many students see motion and think there must be a net force. They might try to use F=ma. But a is acceleration, the change in velocity. Since the velocity is constant, the acceleration is zero! So F_net = m * 0 = 0, which brings us right back to Newton's First Law.
Try it yourself
Ready to test your understanding? Sketch a free-body diagram for each problem first!
- 1The BookshelfA 5.0 kg textbook is sitting on a level bookshelf. A student, Priya, pushes horizontally on the book with a force of 10 N, but the book doesn't move. What is the magnitude of the static friction force acting on the book?
Hint: The key words are "doesn't move." What does this tell you about the book's state of equilibrium and the net force on it?
- 2The SkierA 60 kg skier is gliding down a slope at a constant speed. The slope is angled at 15° to the horizontal. What is the total force of friction and air resistance acting on the skier? (Use g = 9.8 m/s²)
Hint: "Constant speed" means dynamic equilibrium. The net force is zero. But the forces are on an incline! You'll need to analyze the forces parallel to the slope. What component of gravity is pulling the skier down the slope?
Practice — 8 questions
In simple terms, Newton's First Law says an object's motion won't change unless a net force acts on it. An object at rest stays at rest, and an object in motion stays in motion at the same speed and in the same direction.
- 2.4.A: Describe the conditions under which a system's velocity remains constant.
- 2.4.A.1
- The net force on a system is the vector sum of all forces exerted on the system.
- 2.4.A.2
- Translational equilibrium is a configuration of forces such that the net force exerted on a system is zero. Derived equation: ΣF⃗ᵢ = 0
- 2.4.A.3
- Newton's first law states that if the net force exerted on a system is zero, the velocity of that system will remain constant.
- 2.4.A.4
- Forces may be balanced in one dimension but unbalanced in another. The system's velocity will change only in the direction of the unbalanced force.
- 2.4.A.5
- An inertial reference frame is one from which an observer would verify Newton's first law of motion.
flowchart TD
A[Start: Analyze forces on an object] --> B{Is the net force zero? (ΣF = 0)};
B -- Yes --> C{Is the object's initial velocity zero?};
B -- No --> D[Object accelerates (a ≠ 0) --- Newton's 2nd Law];
C -- Yes --> E[Object remains at rest (Static Equilibrium)];
C -- No --> F[Object continues at constant velocity (Dynamic Equilibrium)];
Read what Saavi narrates
Hi everyone, it's Saavi. Let's talk about one of my favorite topics, Newton's First Law.
Have you ever been on a long road trip, driving down a straight highway? You set the cruise control to 65 miles per hour and for miles, the car just... goes. Your foot is off the gas, but the car doesn't slow down, and it doesn't speed up.
The magic of cruise control is that the engine adjusts its push to be exactly equal and opposite to all the forces trying to slow you down, like air resistance. All the forces cancel out.
This state of balanced forces is the core of Newton's First Law. It tells us that when all the forces on an object are perfectly balanced, its motion won't change. We call this 'translational equilibrium'. This can mean the object is at rest, or, like our car on cruise control, it's moving at a constant velocity.
Let's walk through a classic example. Imagine Aaliyah is pushing a 40 kilogram crate across a floor at a constant velocity of 1.5 meters per second. She pushes with a force of 150 Newtons. The question is, what is the force of kinetic friction?
The most important words here are "constant velocity." As soon as you see that, you should think: equilibrium! Acceleration is zero, which means the net force is zero.
So, if Aaliyah is pushing forward with 150 Newtons, there must be another horizontal force pushing back with the exact same strength to keep the net force at zero. That backward force is friction. So, the force of kinetic friction must be 150 Newtons. It's that simple.
Now, here's a common mistake I see every year. Students see an object moving, and they automatically think there must be a net force. But that's not right! A net force causes acceleration... a *change* in velocity. If the velocity is constant, the net force is zero. So please, burn this into your brain: constant velocity means zero net force.
Keep practicing this idea. It's the foundation for everything else we'll do with forces. You've got this.
It has no **net** force. Individual forces, like an engine's push and air resistance, can be present and are simply balanced.
Remember that constant velocity means `ΣF⃗ = 0`. Look for the forces that are canceling each other out.
This is an Aristotelian idea that Newton corrected. Force is required to *change* motion (to accelerate). An object with inertia will maintain its motion on its own if there are no net forces.
Internalize the mantra: "Net force causes acceleration, not velocity."
The physics for an object at rest (static equilibrium) and an object at constant velocity (dynamic equilibrium) is identical: `ΣF⃗ = 0`. They are two sides of the same coin.
When you see "at rest" OR "constant velocity," your first thought should be "Aha! Net force is zero."
Vertical forces can only cancel other vertical forces. Horizontal forces can only cancel other horizontal forces. You can't subtract a downward force of gravity from a rightward push force.
Always create two separate equations: `ΣF_x = 0` and `ΣF_y = 0`. Break all diagonal forces into their x and y components first.
If an object is moving at a constant velocity and you can identify a forward push (like an engine or a person), there *must* be an equal and opposite resistive force to balance it. In the real world, this is almost always friction or drag.
If you see "constant velocity" and an applied force, immediately draw a friction or drag force in the opposite direction on your FBD.