Newton's First Law: Inertia said an object keeps its velocity unless a net force acts. With Free-Body Diagrams, that becomes a tool: whenever the velocity is constant, the forces on the diagram must add to zero.
Key idea
Equilibrium means $\Sigma \vec{F} = 0$, which happens exactly when the velocity is constant: at rest, or moving in a straight line at a steady speed. In components: $\Sigma F_x = 0$ and $\Sigma F_y = 0$.
Why it works
A net force changes velocity; that is what the second law says. So if the velocity isn't changing, there is no net force, whatever the speed. A car cruising at $30\ \text{m/s}$ on a straight road is in equilibrium just as much as a parked car: the forward force from the road exactly balances drag and rolling friction.
- Draw the free-body diagram.
- If the object is at rest or moves at a steady velocity, write $\Sigma F_x = 0$ and $\Sigma F_y = 0$.
- Solve for the unknown force; the speed itself never appears.
Worked examples
Worked example: Constant velocity
You push a $40\ \text{kg}$ crate across a floor at a constant velocity with a $120\ \text{N}$ horizontal push. How big is the friction force?
- Constant velocity: $\Sigma F_x = 0$.
- $120 - f = 0$, so $f = 120\ \text{N}$. The mass isn't needed.
Answer: $120\ \text{N}$
Worked example: Moving, yet balanced
An elevator car of mass $800\ \text{kg}$ rises at a steady $2\ \text{m/s}$. What is the cable's tension?
- Steady velocity, so $\Sigma F_y = 0$: $T - mg = 0$.
- $T = (800)(9.8) = 7{,}840\ \text{N}$, the same as if it were parked.
Answer: $7{,}840\ \text{N}$
Common mistake
Thinking an object moving at a constant speed needs a net force in its direction of motion. That idea fits everyday life, where friction stops things, but the extra push only cancels friction. Check: is the velocity changing? If not, the net force is zero, and the forward forces equal the backward ones.
Try it in the Science Lab: The First Law: Inertia.