AP Physics 1 · Unit 2 · Topic 2.4
Newton’s First Law
In an inertial reference frame, a system's velocity remains constant when the vector sum of all external forces on it is zero. Constant velocity includes the special case of remaining at rest.
Learning Goals
After this lesson, you should be able to:
- state Newton's first law using force and velocity vectors;
- distinguish static from dynamic translational equilibrium;
- calculate a balancing force in one or two dimensions;
- analyze equilibrium independently along perpendicular axes;
- connect force diagrams to position-, velocity-, and acceleration-time graphs;
- explain how mass measures translational inertia; and
- identify whether a reference frame is approximately inertial.
1. The Law of Inertia
Newton's first law states that a system at rest stays at rest and a moving system continues with constant velocity unless a nonzero net external force acts. In vector form,
Constant velocity means constant speed and constant direction. Any speeding up, slowing down, or turning is acceleration and therefore requires a nonzero net external force.
2. Inertia Is Not a Force
Inertia is the tendency of a system to resist a change in its velocity. It is a property, not an arrow to add to a free-body diagram. Translational inertia is measured by mass: a greater mass requires a greater net force to produce the same acceleration.
Mass is not the same as weight. Mass measures inertia in kilograms; weight is a gravitational force measured in newtons.
3. Static and Dynamic Equilibrium
| State | Velocity | Acceleration | Net force |
|---|---|---|---|
| Static equilibrium | \(\vec v=\vec 0\) | \(\vec a=\vec 0\) | \(\sum\vec F=\vec 0\) |
| Dynamic equilibrium | constant and nonzero | \(\vec a=\vec 0\) | \(\sum\vec F=\vec 0\) |
“Equilibrium” does not mean “no forces.” It means all external force vectors sum to zero.
4. Same Force Balance, Two Possible Motions
5. Net Force Is a Vector Sum
Equilibrium requires the sum of all external forces, not merely two conveniently chosen arrows, to vanish:
The force that balances a known resultant \(\vec R\) is the equilibrant:
It has the same magnitude as the resultant and points in the opposite direction.
6. Equilibrium Must Be Checked by Direction
For two-dimensional motion, use independent component conditions:
A system may be balanced vertically while unbalanced horizontally. Its vertical velocity component then remains constant, while its horizontal velocity changes. Never replace two component tests with a visual claim that the diagram “looks balanced.”
7. Worked Example: Constant-Speed Crate
Question: A crate moves right at a constant \(2.5\,\mathrm{m\,s^{-1}}\). A rope pulls right with \(36\,\mathrm N\). Find the horizontal friction force.
Constant velocity means \(a_x=0\), so the horizontal force sum is zero:
Answer: Friction has magnitude \(36\,\mathrm N\) and points left. The crate does not need a rightward net force to maintain rightward motion.
8. Worked Example: Two-Dimensional Balancing Force
Question: Two horizontal forces on a floating sensor platform are \(\vec F_1=(30\hat i+10\hat j)\,\mathrm N\) and \(\vec F_2=(-12\hat i+18\hat j)\,\mathrm N\). What third force keeps its velocity constant?
Answer: The required force is \((-18\hat i-28\hat j)\,\mathrm N\), with magnitude about \(33\,\mathrm N\), directed down and left.
9. Motion Graphs Under Zero Net Force
In one dimension, zero net force implies zero acceleration. The corresponding graph features are:
- Position–time: a straight line with constant slope; a horizontal line is the rest case.
- Velocity–time: a horizontal line, possibly above, below, or on the time axis.
- Acceleration–time: a line on \(a=0\).
A nonzero constant velocity does not require a nonzero force; it requires that no net force change it.
10. Why Everyday Objects Usually Stop
A sliding object on a floor slows because the environment exerts friction and often air drag. Its stopping is evidence of a backward net external force, not evidence that motion naturally “runs out.” Reducing those interactions with wheels, an air track, or a smoother surface makes constant-velocity behavior easier to observe.
11. What Is an Inertial Reference Frame?
An inertial frame is a frame in which an isolated system maintains constant velocity and Newton's first law is verified. A frame moving at constant velocity relative to an inertial frame is also inertial.
For many classroom problems, the ground is an adequate approximation. A car moving straight at constant velocity is also approximately inertial; a car that accelerates, brakes, or turns is not.
12. The Accelerating-Bus Test
A loose ball on the floor of a bus appears to roll backward when the bus accelerates forward. From the ground frame, the ball tends to retain its original velocity while the bus moves forward beneath it. From the accelerating bus frame, the ball seems to accelerate without an identified backward interaction.
That failure of an unmodified first-law description reveals that the bus frame is non-inertial. Do not invent a real backward interaction on the ball's ordinary free-body diagram.
13. Experimental Investigation: Testing Inertia
Use a low-friction cart, motion sensor, and a level track.
- Give the cart a brief push and analyze only the interval after contact ends.
- Graph position, velocity, and acceleration versus time.
- Compare how nearly velocity remains constant with the air track or low-friction system on and off.
- Use a force sensor to estimate the residual horizontal net force.
- Add mass to the cart and repeat the same brief-force protocol, noting which claim concerns inertia and which concerns friction.
Report uncertainty rather than claiming the measured net force is exactly zero.
14. Common Traps and Corrections
- Trap: an object needs a forward force to keep moving. Correction: forward net force changes velocity; zero net force preserves it.
- Trap: equilibrium means rest. Correction: constant nonzero velocity is dynamic equilibrium.
- Trap: zero net force means no forces act. Correction: multiple external forces may vector-sum to zero.
- Trap: inertia is a force opposing motion. Correction: inertia is a property measured by mass.
- Trap: balance along one axis guarantees equilibrium. Correction: check every independent direction.
- Trap: treating observations in an accelerating vehicle as if the frame were inertial. Correction: test whether an isolated object keeps constant velocity.
15. Key Takeaways
- Zero net external force means constant velocity in an inertial frame.
- Rest and uniform straight-line motion are two cases of translational equilibrium.
- Equilibrium is a vector condition that must hold in every direction.
- Mass measures translational inertia; inertia itself is not a force.
- Free-body diagrams predict acceleration, not the velocity already present.
- An inertial frame is one in which Newton's first law is observed to hold.
A puck moves east at constant speed while three horizontal forces act on it: \(12\,\mathrm N\) east, \(5\,\mathrm N\) north, and one unknown force. Determine the unknown force vector and explain whether the puck must be at rest for the forces to be in equilibrium.
Concept scope cross-checked with the College Board AP Physics 1 course framework and the open educational references OpenStax University Physics: Newton's First Law and OpenStax Physics: Newton's First Law and Inertia. Explanations, diagram, examples, and investigation are independently written for Insomnia Studyroom.
Official curriculum reference: College Board AP Physics 1 course page. The explanation and worked example are independently written for this study site.