Newton's First Law — AP Physics 1 Study Guide

For: AP Physics 1 candidates sitting AP Physics 1.

Covers: Inertia as a property of mass, inertial vs non-inertial reference frames, translational equilibrium, net force analysis for equilibrium, and application of Newton’s First Law to 2D static and constant velocity motion problems.

You should already know: How to construct free-body diagrams for systems of forces, how to resolve vectors into perpendicular components, the definition of force and acceleration.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Physics 1 style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Newton's First Law?

Newton’s First Law of Motion, commonly called the Law of Inertia, is a core principle of AP Physics 1 Unit 2: Dynamics, which accounts for 12-18% of the total AP Physics 1 exam score. Newton’s First Law typically appears in both multiple-choice (MCQ) and free-response (FRQ) sections, most often as a foundation for force analysis, though it can also be tested directly in conceptual questions. The formal definition is: A body at rest remains at rest, and a body in motion with constant velocity (constant speed in a straight line) remains in motion with that constant velocity, if and only if the net external force acting on the body is zero. Inertia, the key concept associated with this law, is the tendency of massive objects to resist any change in their state of motion. Newton’s First Law is actually a special case of Newton’s Second Law, when acceleration equals zero (since acceleration is the rate of change of velocity). The AP Physics 1 Course and Exam Description (CED) identifies understanding of Newton’s First Law and equilibrium as a primary learning objective for Unit 2, with direct testing expected on every exam.

2. Inertia and Mass

The most fundamental concept tied to Newton’s First Law is inertia, which is directly proportional to the inertial mass of an object. A common misconception is that inertia is a force; this is incorrect: inertia is a property of all matter with mass, not an interaction between objects, so it never appears on a free-body diagram. Inertial mass measures how much an object resists changing its motion: an object with more mass has more inertia, so it requires a larger net force to produce the same change in velocity (acceleration) as an object with less mass. It is critical to distinguish between mass (inertia) and weight: mass is an invariant property of an object measured in kilograms, while weight is the gravitational force on an object measured in newtons, which varies with gravitational field strength. For example, an astronaut has the same mass (and same inertia) on the Moon as on Earth, even though their weight is 1/6th as large on the Moon. A common question on AP exams asks to compare the inertia of two objects; the correct comparison is always based solely on mass, not weight, speed, or any other property.

Worked Example

Problem: A 1500 kg sedan and a 30,000 kg semi-truck are both at rest on a frictionless horizontal surface. A person pushes both vehicles with the same constant 500 N force for 10 seconds. Using the concept of inertia from Newton’s First Law, compare the final velocity of the two vehicles after 10 seconds.

1. By Newton’s First Law, inertia is the resistance to change in motion, and is directly proportional to inertial mass.
2. Both vehicles start from rest (same initial state of motion), and experience the same net force applied for the same amount of time.
3. The semi-truck has 20 times the mass of the sedan, so it has 20 times the inertia, meaning it resists change in motion 20 times more than the sedan.
4. The larger resistance to acceleration means the semi-truck will gain less velocity over the 10 second interval, resulting in a final velocity that is 1/20th the final velocity of the sedan.

Exam tip: If a question asks you to compare the inertia of two objects, ignore any information about their speed, weight, or location, and only compare their masses. Inertia depends exclusively on inertial mass.

3. Inertial vs Non-Inertial Reference Frames

Newton’s First Law only holds in inertial reference frames, so distinguishing between inertial and non-inertial frames is a key skill for AP Physics 1. A reference frame is just the coordinate system you use to measure position and velocity of objects. An inertial reference frame is any frame that has zero acceleration — that means it is either at rest, or moving at constant velocity relative to another inertial frame. A non-inertial reference frame is any frame that is accelerating (speeding up, slowing down, or turning). In non-inertial frames, you can observe objects accelerating even when the net real force on them is zero, which violates Newton’s First Law. The apparent "forces" you feel in accelerating frames (like the force pushing you back when a car accelerates forward, or the force throwing you forward when a car brakes) are fictitious forces: they are not real forces caused by interactions, just effects of your inertia in an accelerating frame. For example, when a car brakes, you continue moving forward at constant velocity per Newton’s First Law (from the ground’s inertial frame), so you lean forward relative to the accelerating car frame; it looks like a force pushed you, but there is no real force.

Worked Example

Problem: A car is turning left at constant speed around a circular curve. A passenger sitting in the car observes a water bottle on the dashboard sliding to the right relative to the car, with no apparent real force causing it to move. Is the car’s frame of reference inertial? Does Newton’s First Law apply to the water bottle in the car’s frame?

1. A reference frame is inertial only if it has zero net acceleration. The car is turning left, so it has centripetal acceleration toward the left, meaning its acceleration is non-zero.
2. Any accelerating frame is non-inertial, so the car’s frame is not inertial.
3. In the car’s frame, the water bottle accelerates to the right even though there is zero net real force acting on it.
4. Newton’s First Law requires that zero net force corresponds to zero acceleration (constant velocity), which is violated here.
5. Conclusion: The car frame is non-inertial, and Newton’s First Law does not apply to the water bottle in this frame.

Exam tip: Never assume a frame is inertial just because you are observing an object at rest relative to it. Always check if the frame itself is accelerating first.

4. Translational Equilibrium

The most common application of Newton’s First Law on the AP Physics 1 exam is analysis of objects in translational equilibrium. By definition, an object is in translational equilibrium if and only if the net external force on the object is zero, which per Newton’s First Law means the object’s velocity is constant. Equilibrium has two subcategories: static equilibrium, where the object is at rest (velocity = 0), and dynamic equilibrium, where the object moves at constant speed in a straight line. For two-dimensional problems, we can split the net force into x and y components, so the equilibrium condition becomes: $$\sum F_x=0\text{and}\sum F_y=0$$ This system of equations lets you solve for unknown forces, even if you only have constant velocity or rest. A common misconception is that equilibrium means no forces act on the object; that is wrong: multiple forces act, but their vector sum adds up to zero, so no acceleration. To solve equilibrium problems, you first draw a correct free-body diagram, choose a coordinate system, resolve all forces into components, then set the sum of forces on each axis to zero and solve for the unknown.

Worked Example

Problem: A 5.0 kg flower pot is hung at rest from the ceiling by two identical ropes, each making a 45° angle with the horizontal. What is the tension in each rope?

1. The flower pot is at rest, so it is in static equilibrium per Newton’s First Law, so net force is zero.
2. Free-body diagram: weight $mg$ downward, tension $T$ in each rope, each tension pointing up and out at 45°, one to the left and one to the right.
3. Resolve tensions into components: each tension has horizontal component $T\cos 45^{\circ }$ (one left, one right) and vertical component $T\sin 45^{\circ }$ (both up).
4. Sum horizontal forces: $T\cos 45^{\circ }-T\cos 45^{\circ }=0$, which checks out. Sum vertical forces: $2T\sin 45^{\circ }-mg=0$.
5. Solve for $T$: $T=\frac{mg}{2\sin 45^{\circ }}=\frac{(5.0kg)(9.8m/s^2)}{2(\sqrt{2}/2)}=\frac{49}{\sqrt{2}}\approx 35N$.

Exam tip: When solving for tension in symmetric equilibrium problems (like two identical ropes supporting a weight), always use symmetry to simplify the component equations before solving, this saves time on the exam.

5. Common Pitfalls (and how to avoid them)

• Wrong move: Claiming that inertia is a force that keeps objects in motion. Why: Students confuse the property of matter with an interaction force, because they observe that "something has to keep things moving" from everyday experience with friction. Correct move: Always label inertia as a property of mass, not a force, and never include it in a free-body diagram.
• Wrong move: Assuming an object at rest relative to an accelerating frame is in equilibrium per Newton's first law. Why: Students use the object's rest relative to the frame to conclude zero net force, forgetting the frame itself is accelerating. Correct move: First confirm the reference frame is inertial (zero acceleration) before applying Newton's first law to any object in that frame.
• Wrong move: Arguing that a moving object requires a non-zero net force to keep moving. Why: Everyday experience with friction and air resistance leads students to think you need to push to keep moving, forgetting the push is just balancing friction, resulting in zero net force. Correct move: Any object moving at constant velocity has zero net force, regardless of speed; net force is only required to change velocity.
• Wrong move: Comparing inertia based on weight or speed instead of mass. Why: Students think heavier (by weight) or faster moving objects have more inertia, confusing momentum (which depends on speed) with inertia. Correct move: When comparing inertia of two objects, always compare their inertial masses; speed and weight do not affect inertia.
• Wrong move: Concluding that if an object is in equilibrium, all forces on it are equal in magnitude. Why: Students misremember the rule that net force is zero as each force is equal. Correct move: For equilibrium, the vector sum of all forces is zero, not each individual force; you must resolve into components and sum each axis separately.

6. Practice Questions (AP Physics 1 Style)

Question 1 (Multiple Choice)

A box is sliding at constant speed down an inclined plane. Which of the following correctly describes the net force on the box? A) Net force is equal to the component of gravity along the incline, directed down the incline B) Net force is zero because the box moves at constant speed C) Net force is equal to the friction force on the box, directed up the incline D) Net force is directed down the incline, equal to $mg\sin \theta$ minus friction

Worked Solution: Per Newton's First Law, any object moving at constant velocity is in translational equilibrium, which by definition means the net external force on the object is zero. For this box, the component of gravity down the incline is exactly balanced by friction up the incline, and the perpendicular component of gravity is balanced by the normal force from the incline, so the sum of forces in both directions is zero. Options A, C, and D all claim non-zero net force, which is incorrect for constant velocity. The correct answer is B.

Question 2 (Free Response)

A 15 kg sign is hung from two ropes attached to a horizontal ceiling. Rope 1 makes a 30° angle with the ceiling, and Rope 2 makes a 60° angle with the ceiling. The sign is at rest. (a) Draw a free-body diagram for the sign, labeling all real forces. (b) Write the two equilibrium equations (for x and y components of force) based on Newton's First Law, using $T_1$ for tension in Rope 1 and $T_2$ for tension in Rope 2. (c) The weight of the sign is increased by 50% by adding a decoration. Explain how the angles of the two ropes change, if the ropes remain attached to the same points on the ceiling.

Worked Solution: (a) The free-body diagram includes three real forces: 1) Weight $mg$ acting straight downward, 2) Tension $T_1$ acting along Rope 1 (up and to the left at 30° to the horizontal), 3) Tension $T_2$ acting along Rope 2 (up and to the right at 60° to the horizontal). No other forces (including inertia) are included. (b) Choose +x to the right and +y upward. Resolve tensions into components: $T_{1x}=-T_1\cos 30^{\circ }$, $T_{1y}=T_1\sin 30^{\circ }$, $T_{2x}=+T_2\cos 60^{\circ }$, $T_{2y}=T_2\sin 60^{\circ }$. The equilibrium equations per Newton's First Law are: $$\sum F_x=T_2\cos 60^{\circ }-T_1\cos 30^{\circ }=0$$ $$\sum F_y=T_1\sin 30^{\circ }+T_2\sin 60^{\circ }-mg=0$$ (c) The horizontal distance between the two attachment points on the ceiling is fixed. To support the larger weight, the sign will hang lower, which increases the angle each rope makes with the horizontal. A larger angle increases the vertical component of each tension, which is required to balance the larger weight, while the horizontal components of tension remain balanced to satisfy the x-direction equilibrium condition.

Question 3 (Application / Real-World Style)

A cargo train moving at 22 m/s on straight, level tracks cruises at constant velocity. The total mass of the train is $7.5\times 10^5$ kg, and the engine exerts a horizontal pulling force of $1.4\times 10^5$ N to maintain constant speed. What is the total magnitude of resistive forces (rolling friction + air resistance) acting on the train? Interpret your result in context.

Worked Solution:

1. The train moves at constant velocity, so it is in dynamic equilibrium per Newton's First Law, meaning net horizontal force is zero.
2. The horizontal forces acting on the train are the engine's pulling force forward, and total resistive force opposing motion (backward).
3. Sum of horizontal forces: $\sum F_x=F_{pull}-F_{resist}=0⟹F_{resist}=F_{pull}$.
4. Substitute values: $F_{resist}=1.4\times 10^5$ N. Interpretation: The engine's pulling force exactly balances the total resistive force acting on the train, resulting in zero net force, so the train maintains constant speed per Newton's First Law with no acceleration.

7. Quick Reference Cheatsheet

8. What's Next

Newton's First Law is the foundational principle for all of dynamics in AP Physics 1. Immediately after this topic, you will study Newton's Second Law, which generalizes Newton's First Law to cases with non-zero net force and non-zero acceleration. Without mastering equilibrium analysis, the distinction between inertial and non-inertial frames, and the definition of inertia from this chapter, you will not be able to correctly set up force equations for accelerating systems, which account for most of the dynamics unit's exam weight. This topic also underpins concepts later in the course, including circular motion, where you need to distinguish real forces from fictitious inertial effects, and momentum conservation. Follow-on topics to study next: Newton's Second Law, Free-Body Diagram Force Analysis, Translational Equilibrium, Circular Motion Fundamentals