Newton’s First Law of Motion—Inertia: Study Notes

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.

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

• Direction of Natural Motion: On Earth, natural motion is straight up or down; beyond Earth, it is circular (e.g., the Sun and Moon orbiting Earth).

• Violent Motion: Caused by external forces such as pushes or pulls. For example, wind moving a ship.

Galileo's Concept of Inertia

Galileo challenged Aristotle's views in the 1500s, laying the groundwork for modern physics by introducing the concept of inertia.

• 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: Defined as a push or pull.

• Inertia: The property of matter to resist changes in motion, dependent on mass.

• Inclined Plane Experiments: Galileo used inclined planes to show 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

Newton formalized Galileo's findings into 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.

Equation (in words): If the net force $\sum \vec{F} = 0$, then $\vec{v}$ is constant.

Net Force and Vectors

Understanding forces requires the concept of vectors, which have both magnitude and direction.

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

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

• Net Force: The vector sum 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.

Equation: $\sum \vec{F} = \vec{F}_1 + \vec{F}_2 + \ldots$

Vectors: Addition and Resultants

Vectors can be added arithmetically if they are in the same or opposite directions, or using the parallelogram rule if at an angle.

• Resultant: The sum of two or more vectors.

• Pythagorean Theorem (for right angles): $R = \sqrt{A^2 + B^2}$

• Components: Any vector can be broken into components along chosen axes.

Example: A 30-N and a 40-N force 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.

• Static Equilibrium: Object at rest (e.g., a bag of flour hanging from a string).

• Dynamic Equilibrium: Object moving at constant velocity (e.g., a puck sliding at constant speed).

Equation: $\sum \vec{F} = 0$

Support Force (Normal Force)

The support 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 upward force.

• Distribution: If you stand with one foot on each of two scales, each scale reads half your weight.

Equilibrium of Moving Things

Equilibrium applies to both objects at rest and those moving at constant velocity.

• Static Equilibrium: No motion (e.g., crate at rest).

• Dynamic Equilibrium: Constant velocity (e.g., crate pushed at steady speed with applied force equal to friction).

Example: If friction is 75 N, you must apply 75 N to keep the crate moving at constant speed.

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, as do the tree and worm.

• Vehicle 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.