Newton's Laws of Motion

The big idea

You can think of force as a push or a pull, but physics cares about what all the pushes and pulls together do. Newton's laws explain why an object speeds up, slows down, or keeps moving exactly the same way.

Think of motion like a tug-of-war on a shopping cart. If both sides pull equally, the cart does not change speed; if one side pulls harder, the cart changes motion in that direction.

What you'll learn

• What inertia is and why objects resist changes in motion
• How to find net force and use $F_{net}=ma$
• How to read a free-body diagram
• How action-reaction pairs work in Newton's third law

First law: inertia and balanced forces

1. No net force When the forces on an object cancel, the object keeps the same velocity. That means it stays at rest or keeps moving in a straight line at constant speed.
2. Inertia The reason is inertia, the tendency of an object to resist changes in its motion. Bigger mass means more inertia, so it is harder to speed up, slow down, or turn.
3. Seat-belt clue This is why a seat belt matters. When a car stops suddenly, your body wants to keep moving forward. The belt provides the force that changes your motion.

A key idea is that you do not need a force to keep something moving. You need a net force to change its motion.

Second law: net force makes acceleration

1. Add directions Force has direction, so you do not just add sizes. You add them as vectors. The result is the net force, the total force after directions are taken into account.
2. Use the law Newton's second law is $F_{net}=ma$. Here $F$ is in newtons (N), $m$ is in kilograms (kg), and $a$ is in meters per second squared (m/s²). One newton is the force needed to give a 1 kg mass an acceleration of 1 m/s².
3. Choose a sign If you pick right as positive, then left is negative. This keeps the math clean and helps on AP free-response questions.
4. Read the diagram A free-body diagram is a picture of one object with every external force acting on it. The arrows show force directions, not motion directions. This one shows the forces on a box sliding across a floor.

The box is the object. Applied force is 20 N to the right. Friction is 8 N to the left. Weight is 49 N downward because the box has a mass of 5.0 kg. Normal force is 49 N upward from the floor. On a flat floor with no vertical acceleration, weight and normal force balance. In a free-body diagram, you draw only the forces on the box, not the forces the box exerts on the floor.

1. Work it out If right is positive, then $F_{net,x}=20-8=12$ N right and $F_{net,y}=49-49=0$ N. Then $a=F_{net}/m=12/5.0=2.4$ m/s² right. That is how a force diagram turns into motion. Newton's second law tells you how much an object accelerates when you know the net force and the mass.

Third law: action and reaction

1. Equal and opposite Newton's third law says that if object A exerts a force on object B, then object B exerts a force of equal size in the opposite direction on object A.
2. Different objects These forces do not cancel because they act on different objects. That is why a book pushes down on a table while the table pushes up on the book.
3. Common examples When you walk, your foot pushes backward on the ground and the ground pushes forward on you. Rockets work the same way: the rocket pushes exhaust backward, and the exhaust pushes the rocket forward.

Newton's third law is about pairs of forces on two different objects.

Putting it together

Newton's second law and first law fit together like this:

$F_{net}=ma$ If $F_{net}=0$, then $a=0$.

Read it left to right: net force equals mass times acceleration. If the net force is zero, the acceleration is zero.

Worked example: A 5.0 kg box has 20 N pushing right and 8 N friction left. $F_{net,x}=20-8=12$ N right $F_{net,y}=49-49=0$ N $a=F_{net}/m=12/5.0=2.4$ m/s² right

So the box speeds up to the right, but it does not speed up vertically. Acceleration always points in the direction of the net force, even if the object is already moving another way.

Check yourself

1. A hockey puck glides at constant speed on ice. What is the net force on it? Answer Zero, or very close to zero in an ideal model, because constant speed means no acceleration.
2. A 4 kg cart has a net force of 12 N to the left. What is its acceleration? Answer 3 m/s² to the left, because $a=F/m=12/4$.
3. What is the reaction force when Earth pulls down on a falling apple? Answer The apple pulls up on Earth with an equal force.

Common mistakes

• "If an object is moving, there must be a force in the direction of motion." Not necessarily. A moving object with zero net force keeps moving at constant velocity.
• "Action and reaction cancel each other." They do not, because they act on different objects, so they never belong on the same free-body diagram.
• "Mass and weight are the same." Mass is how much matter an object has; weight is the gravitational force on that mass, measured in newtons.

Remember this

• First law: no net force means no change in motion.
• Second law: $F_{net}=ma$.
• Third law: forces come in equal-and-opposite pairs on different objects.