Newton's First Law

AP Physics 1· AP Physics 1 CED — Dynamics· 14 min read

1. Newton's First Law and Inertia★★☆☆☆⏱ 4 min

Newton’s First Law of Motion (also called the Law of Inertia) is a core principle of AP Physics 1 Unit 2 Dynamics, which makes up 12-18% of total exam score. 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.

📘 Definition

Inertia

Inertia $\propto m$

The tendency of a massive object to resist any change in its state of motion. Inertia is a property of matter, not a force, and is directly proportional to an object's inertial mass.

Example:

A 10 kg object has twice the inertia of a 5 kg object, regardless of speed or location.

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. An astronaut has the same mass (and same inertia) on the Moon as on Earth, even though their weight is only 1/6th as large.

📐 Worked Example

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:
5
$v_{\text{semi}} = \frac{1}{20} v_{\text{sedan}}$

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.

2. Inertial vs Non-Inertial Reference Frames★★★☆☆⏱ 3 min

Newton’s First Law only holds in inertial reference frames, so distinguishing between the two frame types is a key AP Physics 1 skill. A reference frame is the coordinate system you use to measure position and velocity of objects.

📘 Definition

Reference Frame Classification

An inertial reference frame has zero acceleration (at rest or constant velocity relative to other inertial frames), where Newton's First Law is valid. A non-inertial frame is accelerating, so Newton's First Law does not hold.

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. Apparent "forces" you feel in accelerating frames (like being pushed back when a car accelerates) are fictitious forces: they are not real interaction forces, just effects of your inertia in an accelerating frame.

📐 Worked Example

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.

3. Translational Equilibrium★★★☆☆⏱ 5 min

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 (object at rest, $v = 0$ ) and dynamic equilibrium (object moving at constant speed in a straight line).

\sum F_x = 0 \quad \text{and} \quad \sum F_y = 0

A common misconception is that equilibrium means no forces act on the object; this is incorrect: 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

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, meaning net force is zero.
2
Free-body diagram: weight $m g$ 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 $T cos 4 5^{\circ}$ (one left, one right) and vertical component $T sin 4 5^{\circ}$ (both up).
4
Sum horizontal forces: $T cos 4 5^{\circ} - T cos 4 5^{\circ} = 0$ , which satisfies equilibrium. Sum vertical forces:
5
$2 T \sin 45^\circ - mg = 0$
6
Solve for $T$ :
7
$T = \frac{mg}{2 \sin 45^\circ} = \frac{(5.0 kg)(9.8 m/s^2)}{2 (\sqrt{2}/2)} = \frac{49}{\sqrt{2}} \approx 35 N$

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.

4. AP-Style Concept Check★★★☆☆⏱ 2 min

✓ Quick check

Test your understanding of Newton's First Law with these AP-style questions:

A box is sliding at constant speed down an inclined plane. Which of the following correctly describes the net force on the box?
- Net force is equal to the component of gravity along the incline, directed down the incline
- Net force is zero because the box moves at constant speed
- Net force is equal to the friction force on the box, directed up the incline
- Net force is directed down the incline, equal to $m g sin θ$ minus friction
Reveal answer
1 —
Per Newton's First Law, any object moving at constant velocity is in translational equilibrium, which by definition means net external force is zero. The component of gravity down the incline is exactly balanced by friction, and perpendicular gravity is balanced by normal force, so sum of forces is zero.
A cargo train moving at 22 m/s on straight, level tracks cruises at constant velocity. The total mass of the train is $7.5 \times 1 0^{5}$ kg, and the engine exerts a horizontal pulling force of $1.4 \times 1 0^{5}$ N to maintain constant speed. What is the total magnitude of resistive forces acting on the train?
Reveal answer
$1.4 \times 10^5$ N —
The train moves at constant velocity, so it is in dynamic equilibrium, meaning net horizontal force is zero. The pulling force forward equals the resistive force backward, so resistive force equals the pulling force magnitude.

5. Common Pitfalls

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 everyday experience with friction creates the misconception that 'something has to keep things moving'.

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 to get 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 individual force being 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. Quick Reference Cheatsheet

Category	Formula / Rule	Notes
Newton's First Law (General)	If $\sum F_{e x t} = 0$ , then $v = constant$	Only holds in inertial reference frames; applies to both rest and constant velocity.
Inertia	Inertia $\propto m$	Property of matter, not a force; depends only on mass, not speed or weight.
Inertial Reference Frame	$a_{f r am e} = 0$	Frame is at rest or moving at constant velocity; Newton's First Law is valid here.
Non-Inertial Reference Frame	$a_{f r am e} \neq = 0$	Accelerating frame; Newton's First Law does not hold; apparent 'fictitious forces' are just inertia effects.
Translational Equilibrium	$\sum F_{e x t} = 0$	Defined by Newton's First Law; includes both static and dynamic equilibrium.
2D Equilibrium (Component Form)	$\sum F_{x} = 0, \sum F_{y} = 0$	Resolve all forces into components before summing; works for any 2D equilibrium problem.
Static Equilibrium	$v = 0, \sum F_{e x t} = 0$	Object at rest; special case of translational equilibrium.
Dynamic Equilibrium	$v = constant, \sum F_{e x t} = 0$	Object moving at constant speed in a straight line; special case of equilibrium.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · 1
MCQ comparing inertia of two objects
2022 · 1
FRQ 2D equilibrium problem

What's Next

Newton's First Law is the foundational principle for all of dynamics in AP Physics 1. It establishes the framework for all force analysis, and every other Newton's law builds on the core concepts you learned here: the definition of inertia, the equilibrium condition, and the importance of inertial reference frames. Without mastering equilibrium analysis and the definition of inertia from this topic, 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 later concepts including circular motion, where you will need to distinguish real forces from fictitious inertial effects, and momentum conservation.