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 and violent. These ideas influenced scientific thought for centuries until challenged by later scientists.

• Natural motion: Objects move to their 'proper place' determined by the four elements: earth, water, air, and fire. For example, stones fall and smoke rises.

• Natural motion on Earth: Always straight up or down.

• Natural motion beyond Earth: Circular, such as the Sun and Moon orbiting Earth.

• Violent motion: Caused by external forces (pushes or pulls), e.g., wind moving a ship.

Galileo's Concept of Inertia

Galileo Galilei revolutionized the understanding of motion by introducing the concept of inertia and disproving Aristotle’s assertions.

• Key discoveries:

  • Objects of different weights fall at the same rate in the absence of air resistance.

  • A moving object does not require a force to keep moving if friction is absent.

• Force: A push or pull acting on an object.

• Inertia: The property of matter to resist changes in motion; depends on mass.

• Inclined plane experiments: Showed that objects maintain motion unless acted upon by friction.

Example: A ball rolling on a horizontal plane continues at constant speed unless friction slows it down.

Newton's First Law of Motion

Isaac Newton formalized the concept of inertia in his First Law of Motion, also known as the Law of Inertia.

• Statement: Every object continues in a state of rest or uniform motion in a straight line unless acted on by a nonzero net force.

Mathematical form:

Net Force and Vectors

The net force is the vector sum of all forces acting on an object. Forces are vector quantities, meaning they have both magnitude and direction.

• Vector: Quantity with magnitude and direction (e.g., force, velocity, acceleration).

• Scalar: Quantity with magnitude only (e.g., mass, speed, volume).

• Net force: The combination of all forces acting on an object.

Examples:

• Two 5-N forces in the same direction: net force is 10 N.

• Two 5-N forces in opposite directions: net force is 0 N.

• 15 N right and 20 N left: net force is 5 N to the left.

Vectors: Addition and Resultants

Vectors can be added arithmetically if they are in the same or opposite directions. For vectors at angles, use the parallelogram rule or Pythagorean theorem for right angles.

• Resultant: The sum of two or more vectors.

• Pythagorean theorem for right-angle vectors:

Example: 30-N and 40-N vectors at right angles have a resultant of 50 N.

The Equilibrium Rule

An object is in equilibrium when the vector sum of all forces acting on it is zero. This applies to both objects at rest (static equilibrium) and objects moving at constant velocity (dynamic equilibrium).

• Equilibrium rule (mathematical form):

Example: A bag of flour hanging from a string is at rest because the upward tension balances the downward weight.

Support Force (Normal Force)

The support force is the upward force that balances the weight of an object on a surface. It is also called the normal force.

• Example: A book on a table compresses the table slightly, and the table pushes back with an equal upward force.

• When standing on two scales: Each scale reads half your weight if your weight is evenly distributed.

Equilibrium of Moving Things

Equilibrium can be static (object at rest) or dynamic (object moving at constant velocity). In both cases, the net force is zero.

• Static equilibrium: No motion (e.g., puck at rest).

• Dynamic equilibrium: Constant velocity (e.g., puck sliding at constant speed).

• Test for equilibrium: If there is no change in motion, the object is in equilibrium.

Example: If you push a crate at steady speed and friction is 75 N, you must apply 75 N of force.

The Moving Earth

Copernicus proposed that Earth moves around the Sun. Inertia explains why objects on Earth move with it.

• Example: A bird swooping from a branch moves with the Earth and lands where expected.

• Example: Tossing a coin straight up in a moving vehicle: the coin lands back in your hand because it retains the vehicle’s horizontal motion.