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, , 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 , , and .
Key Facts
- Newton's first law says that if , then and an object remains at rest or moves with constant velocity.
- Newton's second law is , 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: .
- Weight is the gravitational force on an object, with magnitude , where near Earth .
- On a horizontal surface with no vertical acceleration and no other vertical forces, the normal force is .
- Kinetic friction has magnitude and points opposite the direction of sliding motion.
- Static friction adjusts as needed up to a maximum value, so .
- 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, .
- Net Force
- Net force is the vector sum of all forces on an object, written as .
- 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 .
- Treating mass and weight as the same thing is wrong because mass is measured in while weight is a force given by .
- Assuming the normal force always equals is wrong because angled surfaces, extra vertical pulls, or vertical acceleration can change .
- Putting action and reaction forces on the same free-body diagram is wrong because Newton's third law forces act on different objects.
- Using for static friction is wrong because static friction can be any value up to .
Practice Questions
- 1 A box is pulled right with while friction pushes left with . Find the net force and acceleration.
- 2 A crate slides across a horizontal floor with . Using , find and .
- 3 A person stands in an elevator accelerating upward at . 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.
Understanding Newton's Laws & Forces
A force is an interaction, not a property stored inside an object. A book on a table has weight because Earth pulls it. The table pushes upward on the book because the book presses on the table.
These forces have different sources, so naming the source helps prevent mistakes. When a person kicks a ball, the foot acts only while contact lasts.
After the kick, the ball can keep moving even though the foot is no longer touching it. Its later motion depends on forces such as air resistance, gravity, or contact with the ground.
A careful free body diagram begins by choosing one object. Draw that object as a dot or box. Then include only forces exerted on it by something outside it.
Do not draw forces that the object exerts on other things. Choose coordinate directions that fit the motion or surface. For a ramp, one direction along the ramp and one perpendicular to it usually makes the work simpler.
Weight always points straight toward Earth’s center. The normal force points perpendicular to the contact surface, not automatically straight upward. A sloping surface changes the direction of the normal force.
Forces must be combined separately in each chosen direction. A force at an angle can be split into two parts. One part affects motion along the surface.
The other part affects motion away from or into the surface. These parts are called components. A box pulled by a rope at an upward angle may have less normal force than a box pulled horizontally.
That can reduce friction because friction depends on how strongly the surfaces press together. This explains why lifting slightly on a heavy suitcase handle can make it easier to pull.
Friction deserves special attention because it does not always have one fixed value. Static friction prevents relative sliding. It takes whatever amount is needed to keep an object from slipping, until it reaches its limit.
A parked car on a hill may be held still by static friction. If the downhill pull becomes too large, the tires slide and kinetic friction takes over.
Kinetic friction often has a smaller size, which is one reason an object can start moving suddenly after it begins to slip. Friction points against the actual sliding direction or the direction the surfaces would slide relative to each other.
Newton’s third law pairs are often confused with forces that cancel. A force pair acts on two separate objects, so the pair cannot cancel within one free body diagram. For example, a swimmer pushes water backward while water pushes the swimmer forward.
In problems with ropes, pulleys, or connected carts, list each object separately before linking their motions. Objects connected by a taut rope usually share related accelerations. Check units, directions, and signs at the end.
A negative acceleration does not mean an object is moving backward. It means the acceleration points opposite to the direction chosen as positive.