Newtonian Mechanics
Newton's three laws of motion, first published in his Principia Mathematica in 1687, form the foundation of classical mechanics. These laws describe the relationship between a body and the forces acting upon it, and its motion in response to those forces.
Newton's First Law of Motion
The Law of Inertia
An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
Key Points:
- Inertia is the tendency of objects to resist changes in their state of motion
- The more mass an object has, the greater its inertia
- This law defines what we mean by an inertial reference frame
A book lying on a table remains at rest because the gravitational force (pulling it down) is exactly balanced by the normal force (pushing it up) from the table. The net force is zero, so the book doesn't accelerate.
When a car stops suddenly, passengers continue moving forward at the car's original speed (due to inertia). Seat belts provide the unbalanced force needed to bring passengers to rest relative to the car, preventing injury.
Newton's Second Law of Motion
The Law of Acceleration
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Key Points:
- This is a vector equation - direction matters
- Force causes acceleration, not velocity
- The SI unit of force is the Newton (1 N = 1 kg·m/s²)
When you push a shopping cart with a constant force, the cart accelerates. A heavier cart (greater mass) will accelerate less than a lighter one under the same force. If you push twice as hard, the acceleration doubles (assuming mass stays constant).
Rockets work by expelling mass (exhaust gases) at high velocity. According to Newton's second law, the force (thrust) equals the rate of change of momentum of the exhaust gases (F = dp/dt). This creates an equal and opposite force that propels the rocket forward.
Newton's Third Law of Motion
The Law of Action-Reaction
For every action, there is an equal and opposite reaction.
Key Points:
- The two forces act on different objects
- The forces are equal in magnitude but opposite in direction
- Both forces exist simultaneously
When you walk, your foot pushes backward against the ground (action), and the ground pushes forward on your foot (reaction). It's this forward force from the ground that propels you forward.
A helicopter's rotor blades are shaped to push air downward (action). By Newton's third law, the air pushes upward on the rotor blades with an equal force (reaction), creating lift that keeps the helicopter airborne.
