BackNewton's First Law of Motion—Inertia: Foundations, Forces, and Equilibrium
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Chapter 2: Newton's First Law of Motion—Inertia
Aristotle's Ideas of Motion
Early concepts of motion were shaped by Aristotle, who classified motion into two types: natural motion and violent motion.
Natural motion: Objects move toward their 'natural place' determined by the four elements (earth, water, air, fire). For example, stones fall to the ground, and smoke rises.
Violent motion: Motion caused by external forces, such as wind pushing a ship.
Aristotle believed that all motion on Earth was straight up or down, while celestial motion was circular.
Galileo's Concept of Inertia
Galileo challenged Aristotle's views in the 1500s, laying the groundwork for modern physics. He demonstrated that objects of different weights fall at the same rate in the absence of air resistance and that a force is not needed to keep an object moving if friction is absent.
Inertia: The property of matter to resist changes in motion. It depends on the mass of the object.
Galileo used inclined planes to show that balls rolling down a slope speed up, up a slope slow down, and on a flat surface maintain their speed unless acted upon by friction.
Newton's First Law of Motion
Building on Galileo's work, Newton formulated the First Law of Motion (Law of Inertia):
Every object continues in a state of rest or uniform motion in a straight line unless acted upon by a nonzero net force.
This law explains why objects remain at rest or in constant motion unless a force causes a change.
Net Force and Vectors
The concept of net force is central to understanding motion. Forces are vector quantities, meaning they have both magnitude and direction.
Net force: The combination of all forces acting on an object. If forces are in the same direction, they add; if opposite, they subtract.
Examples: Two 5-N forces in the same direction yield a 10-N net force; in opposite directions, the net force is zero.
Vectors and Scalars
Physical quantities can be classified as vectors or scalars:
Vector quantity: Has both magnitude and direction (e.g., force, velocity, acceleration). Represented by arrows.
Scalar quantity: Has only magnitude (e.g., mass, speed, volume).
Resultant: The sum of two or more vectors. For perpendicular vectors, use the Pythagorean theorem:
The Equilibrium Rule
An object is in equilibrium when the vector sum of all forces acting on it is zero. This can occur whether the object is at rest (static equilibrium) or moving at constant velocity (dynamic equilibrium).
Mathematical form:
Example: A bag of flour hanging from a string is at rest because the upward tension equals the downward force of gravity.
Support Force (Normal Force)
The support force (or normal force) is the upward force that balances the weight of an object on a surface.
Example: A book on a table compresses the table slightly, and the table pushes back with an equal and opposite force.
When standing on two scales, each scale supports half your weight if your weight is evenly distributed.
Equilibrium of Moving Things
Equilibrium applies to both stationary and moving objects. If an object moves at constant velocity, the forces acting on it are balanced.
Static equilibrium: No motion (e.g., a hockey puck at rest).
Dynamic equilibrium: Constant velocity (e.g., a puck sliding at constant speed).
Test for equilibrium: If there is no change in motion, the object is in equilibrium.
To maintain constant velocity against friction, the applied force must equal the friction force.
The Moving Earth and Inertia
Copernicus proposed that Earth moves around the Sun. Critics questioned how objects could move with Earth. The answer lies in inertia: objects on Earth share its motion and continue moving with it unless acted upon by another force.
Example: A bird swooping from a branch to catch a worm moves with the Earth, as do the tree and worm.
If you toss a coin straight up in a moving vehicle, it lands back in your hand because it retains the vehicle's horizontal motion.
