Start with the force diagram

First, put the equation aside

Imagine a book sitting on a table. It is not moving. Does that mean no forces act on it?

Take a moment to sketch your answer before reading on.

The Earth pulls the book downward. The table pushes it upward. Those interactions are present even though the book stays still. The useful question is not “Is anything moving?” but “What is interacting with the object?”

Choose one object

Draw a dot or a small box to represent the book. Everything else—the Earth, the table, your hand if you are touching it—belongs outside this chosen system.

Now list the interactions that cross that boundary:

• Earth on book: gravity, drawn downward.
• Table on book: a contact force perpendicular to the table, drawn upward.

Label the arrows $mg$ and $N$. The symbol $N$ here means the normal force; the unit newton is also written $\mathrm{N}$.

Every arrow needs a source. If you cannot name the object exerting a force, question the arrow.

Connect the diagram to motion

Take upward as positive. Newton’s second law gives

$$\sum F_y = N - mg = ma_y.$$

The book stays at rest, so $a_y = 0$. Therefore $N = mg$.

Notice the order: we identified the forces, chose a direction, and used the motion to determine their relationship. The normal force equals the weight in this situation. That is a conclusion, not a rule for every contact problem.

Avoid an extra force

The book also pushes downward on the table. Should that force appear on the book’s diagram?

Check your reasoning

No. That force acts on the table. A free-body diagram contains only forces acting on the chosen object.

The upward normal force on the book and the downward contact force on the table form a Newton’s-third-law pair. The book’s weight and its normal force do not: they both act on the same object.

Try it on paper

Draw the book’s diagram again without looking. Beside each arrow, write “___ acts on the book.”

Then try A book at rest. If you want another view of contact forces, open the reading in the related resources. When the diagram feels comfortable, continue to choosing axes for a slope.