Newton's three laws (1687) remain the foundation of classical mechanics for everyday speeds and macroscopic objects.
First Law: The Law of Inertia
An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted upon by an unbalanced external force.
Implications
- A book on a table remains at rest until a net force acts
- On a nearly frictionless surface, a puck continues at nearly constant velocity
- In a braking vehicle, unrestrained objects continue forward relative to the cabin (inertia)
Key Concept: Inertia
Inertia is resistance to changes in motion. Greater mass means greater inertia.
Second Law: F = ma
The acceleration of an object equals the net force acting on it divided by its mass.
F = ma (or equivalently, a = F/m)
Where:
- F = net force (in Newtons, N)
- m = mass (in kilograms, kg)
- a = acceleration (in m/s²)
Example: Pushing a Shopping Cart
A 20 kg shopping cart is pushed with a force of 40 N. What is its acceleration?
- a = F/m = 40 N / 20 kg = 2 m/s²
Important Notes
- Net force means the sum of ALL forces. If friction pushes back at 10 N while you push forward at 40 N, the net force is 30 N.
- Force and acceleration are vectors — direction matters!
- Weight is a force: W = mg (where g ≈ 9.81 m/s²)
Third Law: Action and Reaction
For every action, there is an equal and opposite reaction.
What It Really Means
When you push a wall, the wall pushes back on you with the exact same force. The key insight: action-reaction pairs act on different objects.
Examples
| Action | Reaction |
|---|---|
| You push the ground backward (walking) | Ground pushes you forward |
| Rocket expels exhaust downward | Exhaust pushes rocket upward |
| Ball hits a bat | Bat hits the ball back |
Common Misconception
"If forces are equal and opposite, how does anything move?" — Because the forces act on different objects. When you push a box, you exert force on the box (it accelerates) and the box exerts force on you (but you're heavier, so you don't move much).
Free Body Diagrams
A free body diagram (FBD) shows all forces acting on a single object. It's the key tool for solving Newton's law problems:
- Identify the object of interest
- Draw it as a dot (or simple shape)
- Draw arrows for each force (weight, normal, friction, applied, tension)
- Label each force with its magnitude or variable name
- Choose a coordinate system (usually x horizontal, y vertical)
- Apply F = ma in each direction
Solving Problems with Newton's Laws
Step-by-step approach:
- Draw a free body diagram
- Choose your coordinate system
- Write ΣF = ma for each axis
- Substitute known values
- Solve for unknowns
- Check: Does the answer make physical sense?
Example: Block on an Inclined Plane
A 10 kg block slides down a frictionless 30° incline. Find its acceleration.
- Forces: Weight (mg) down, Normal force (N) perpendicular to surface
- Along the incline: mg sin(30°) = ma
- a = g sin(30°) = 9.81 × 0.5 = 4.905 m/s²
Practice Problems
- A 5 kg object experiences a net force of 25 N. What is its acceleration?
- A 1000 kg car brakes from 20 m/s to 0 in 5 seconds. What braking force is applied?
- Two blocks (3 kg and 5 kg) are connected by a string on a frictionless surface. A 16 N force is applied. Find the acceleration and tension.
Try It Yourself
Use the interactive Newton's Laws tool to check F = ma problems:
Use our Kinematics Calculator and Newton's Laws Tool to check your answers and explore motion problems interactively.