Newton's Laws & Forces Cheat Sheet

A printable reference covering Newton's laws, net force, free-body diagrams, friction, weight, normal force, tension, and acceleration for grades 9-10.

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Newton's laws and forces explain how objects start moving, stop moving, speed up, slow down, or stay at rest. This cheat sheet helps students connect everyday motion to force diagrams and equations. It is useful for solving problems involving pushes, pulls, friction, weight, normal force, and tension. Students need these tools to turn word problems into clear physics models. The central idea is that motion changes only when there is a nonzero net force. Newton's second law, $\sum \vec{F}=m\vec{a}$ , connects total force, mass, and acceleration. Free-body diagrams show every force acting on one object so that forces can be added by direction. Common formulas include $F_g=mg$ , $f_k=\mu_k F_N$ , and $f_s\le \mu_s F_N$ .

Key Facts

Newton's first law says that if $\sum \vec{F}=0$ , then $\vec{a}=0$ and an object remains at rest or moves with constant velocity.
Newton's second law is $\sum \vec{F}=m\vec{a}$ , so acceleration points in the same direction as the net force.
Newton's third law says forces come in equal and opposite pairs on different objects: $\vec{F}_{A\text{ on }B}=-\vec{F}_{B\text{ on }A}$ .
Weight is the gravitational force on an object, with magnitude $F_g=mg$ , where near Earth $g\approx 9.8\,\text{m/s}^{2}$ .
On a horizontal surface with no vertical acceleration and no other vertical forces, the normal force is $F_N=mg$ .
Kinetic friction has magnitude $f_k=\mu_k F_N$ and points opposite the direction of sliding motion.
Static friction adjusts as needed up to a maximum value, so $f_s\le \mu_s F_N$ .
Tension acts along a rope or string, and for an ideal massless rope over an ideal pulley, the tension magnitude is the same throughout the rope.

Vocabulary

Force: A force is a push or pull on an object, measured in newtons, $\text{N}$ .
Net Force: Net force is the vector sum of all forces on an object, written as $\sum \vec{F}$ .
Inertia: Inertia is the tendency of an object to resist changes in its motion, and greater mass means greater inertia.
Free-Body Diagram: A free-body diagram is a drawing that shows one object and all external forces acting on it.
Normal Force: The normal force is the support force exerted by a surface perpendicular to that surface.
Friction: Friction is a contact force that opposes sliding motion or the tendency to slide between surfaces.

Common Mistakes to Avoid

Adding forces without directions is wrong because force is a vector. Choose positive and negative directions before using $\sum F=ma$ .
Treating mass and weight as the same thing is wrong because mass is measured in $\text{kg}$ while weight is a force given by $F_g=mg$ .
Assuming the normal force always equals $mg$ is wrong because angled surfaces, extra vertical pulls, or vertical acceleration can change $F_N$ .
Putting action and reaction forces on the same free-body diagram is wrong because Newton's third law forces act on different objects.
Using $f_k=\mu_k F_N$ for static friction is wrong because static friction can be any value up to $f_s\le \mu_s F_N$ .

Practice Questions

1 A $5.0\,\text{kg}$ box is pulled right with $30\,\text{N}$ while friction pushes left with $10\,\text{N}$ . Find the net force and acceleration.
2 A $12\,\text{kg}$ crate slides across a horizontal floor with $\mu_k=0.20$ . Using $g=9.8\,\text{m/s}^{2}$ , find $F_N$ and $f_k$ .
3 A $70\,\text{kg}$ person stands in an elevator accelerating upward at $1.5\,\text{m/s}^{2}$ . Find the normal force on the person.
4 A book rests on a table. Explain why the book can have forces acting on it even though it is not accelerating.