Three laws that explain motion
In 1687, Isaac Newton published Principia Mathematica, describing three laws of motion. They explain everything from a rolling ball to a rocket launch, and they’re still used to plan spacecraft paths today.
Newton’s first law: inertia
Newton’s first law: an object at rest stays at rest, and an object in motion keeps moving at constant velocity, unless acted on by a net force.
This tendency to resist change is inertia. Mass is a measure of inertia.
| Example | Explanation |
|---|---|
| Passengers lurch forward when a car brakes | Their bodies keep moving forward |
| A tablecloth can be yanked from under dishes | The dishes’ inertia keeps them in place |
| A hockey puck glides far on ice | Very little friction to stop it |
| Spacecraft coast through space without engines | No significant forces to slow them |
Before Newton (and Galileo), people believed objects naturally slow down and stop. Newton realized that they stop only because of forces like friction.
Newton’s second law: F = ma
Newton’s second law:
F_net = ma
- F_net is the net force (N)
- m is mass (kg)
- a is acceleration (m/s²)
The acceleration is in the same direction as the net force.
Examples:
- A 0.15 kg baseball accelerated at 400 m/s² needs F = 0.15 × 400 = 60 N.
- A 70 kg skater pushed with 140 N net force accelerates at a = 140 ÷ 70 = 2 m/s².
Solving force problems
- Draw a free-body diagram showing every force.
- Choose positive directions.
- Add forces to find the net force in each direction.
- Apply F_net = ma.
Common forces
| Force | Symbol | Direction |
|---|---|---|
| Weight (gravity) | F_g = mg | Down |
| Normal force | F_N | Perpendicular away from the surface |
| Friction | F_f | Opposite to motion or attempted motion |
| Tension | F_T | Along a rope, away from the object |
| Applied force | F_a | Whatever direction it’s applied |
Friction
- Static friction prevents an object from starting to move. Its maximum is μ_s F_N.
- Kinetic friction acts on sliding objects: F_f = μ_k F_N.
- μ (mu) is the coefficient of friction. Rubber on dry concrete: μ_k ≈ 0.7. Steel on ice: μ_k ≈ 0.03.
Example: A 20 kg box is pushed with 100 N across a floor where μ_k = 0.3.
- F_N = mg = 20 × 9.8 = 196 N
- F_f = 0.3 × 196 = 58.8 N
- F_net = 100 − 58.8 = 41.2 N
- a = 41.2 ÷ 20 = 2.06 m/s²
Newton’s third law: action and reaction
Newton’s third law: for every action force, there is an equal and opposite reaction force.
Forces always come in pairs acting on different objects.
| Action | Reaction |
|---|---|
| Your foot pushes back on the ground | The ground pushes you forward |
| A rocket pushes exhaust gas down | The gas pushes the rocket up |
| A swimmer pushes water backward | The water pushes the swimmer forward |
| Earth pulls you down (your weight) | You pull Earth up with an equal force |
Why don’t they cancel? Because they act on different objects. To find an object’s acceleration, include only the forces acting on that object.
If both forces are equal, why does Earth not move toward you? It does, but its mass is so huge (6 × 10²⁴ kg) that its acceleration is immeasurably tiny.
Applying all three laws: a car crash
- First law: an unbelted passenger keeps moving forward when the car stops.
- Second law: an airbag increases the time to stop, lowering the deceleration and the force on the body.
- Third law: the car pushes on the wall, and the wall pushes back equally on the car.
Common mistakes
- Thinking a moving object needs a constant force to keep moving.
- Cancelling third-law pairs. They act on different objects.
- Using total force instead of net force in F = ma.
Try it yourself
- A 1500 kg car accelerates at 3 m/s². What net force acts on it?
- A 5 kg sled is pulled with 30 N; friction is 10 N. What is its acceleration?
- Identify the action–reaction pair when a book rests on a table.
- Why is it harder to stop a loaded truck than an empty one at the same speed?
(Answers: 4500 N; 4 m/s²; the book pushes down on the table, the table pushes up on the book; the loaded truck has more mass and so more inertia)
Quick recap
- First law: objects resist changes in motion (inertia).
- Second law: F_net = ma.
- Third law: forces come in equal and opposite pairs on different objects.
- Free-body diagrams help find the net force.
- Friction depends on the normal force and the coefficient of friction.