Topic 2.4 Newton's First Law: state Newton's first law, relate it to inertia, and apply the condition of zero net force to objects in translational equilibrium.

What this topic is asking

The College Board (Topic 2.4) wants you to state Newton's first law, connect it to the idea of inertia, and apply the zero-net-force condition to objects in translational equilibrium (at rest or moving at constant velocity). The recurring exam skill is recognizing that constant velocity means balanced forces, and using that to solve for unknown forces.

Newton's first law and inertia

The first law overturns the everyday intuition that motion needs a continuous push. In reality, a moving object slows down only because of forces like friction; remove those, and it coasts forever. The more massive an object, the more inertia it has, and the harder it is to start, stop, or turn.

Equilibrium: the zero-net-force condition

This single condition solves a large class of problems. Whenever an object is at rest or moving steadily, you know the forces must add to zero, so you can set up balance equations on each axis and solve for unknown tensions, normal forces, or applied forces.

Applying equilibrium

The standard routine is the free-body diagram from Topic 2.2, followed by two balance equations:

• Resolve every force into $x$- and $y$-components.
• Set the sum of $x$-components to zero and the sum of $y$-components to zero.
• Solve the two equations for the unknowns.

For a hanging sign, a box on a ramp held in place, or a person standing still, the physics is the same: balanced forces. The first law guarantees that constant velocity (including zero velocity) means balance, so you never need to know the acceleration; it is zero by assumption.

Why "no force needed for motion" is the key insight

The deepest idea in this topic is that force changes motion rather than sustains it. A spacecraft far from any star keeps drifting at constant velocity with its engines off, because nothing acts to slow it. On Earth, the reason a pushed book stops is friction, an external force, not the absence of a "driving" force. This reframing matters because it tells you exactly when forces must balance: any time the velocity is not changing. It also underlies the seatbelt: when a car stops suddenly, your body's inertia keeps it moving forward at the old velocity until a force (the belt) acts to change that motion. Recognizing constant velocity as a force-free (net-zero) condition, and acceleration as the signature of an unbalanced force, is the bridge from the first law to the second law in the next topic. Equilibrium problems are essentially second-law problems with the acceleration set to zero, so mastering them here makes the general case straightforward.

Try this

Q1. A lamp hangs at rest from a single vertical cord. If the lamp weighs $25$ N, calculate the tension in the cord. [2 points]

• Cue. Equilibrium: tension equals weight, so $T = 25$ N.

Q2. State what the net force must be on a car cruising at a steady $100$ km/h on a straight, level road. [1 point]

• Cue. Zero, because the velocity is constant (the driving force balances drag and friction).