Motion and Forces — Quick Reference

Natural motion: objects have a proper place (earth, water, air, fire) and strive to reach it; natural motion on Earth is straight, beyond Earth is circular.
Violent motion: produced by external pushes or pulls.

Objects of different weights fall at the same time in the absence of air resistance.
A moving object needs no force to keep moving in the absence of friction.
Inclined planes show: downward slopes add speed at the same rate for all balls; upward slopes slow them at the same rate; on a frictionless horizontal plane, speed remains constant.
Inertia: property of matter to resist changes in motion; depends on mass.
Galileo emphasized removing medium/friction to reveal the essence of motion.

Copernicus proposed Earth moving around the Sun; inertia keeps objects moving with Earth unless acted on.
Dropping a rock from rest keeps it moving with Earth's rotation while it falls.
In a moving vehicle, a tossed coin lands in your hand (demonstrates inertia).
Foucault's pendulum demonstrates Earth's rotation.

Model: Motion = Prediction via Cause and Effect; 3 laws.
1st Law: If F_net = 0, velocity is constant (rest or straight-line motion).
2nd Law: $F_{net} = ma$
3rd Law: Action–reaction pairs are equal and opposite, acting on different objects.

A force is a push or pull; acts on an object; is a vector with magnitude and direction; two types: contact and long-range.
Net force is the vector sum of all forces on an object.
Examples: two 5-N pulls in the same direction give a 10-N net; opposite directions cancel to 0.
Force vectors are represented by arrows: length = magnitude, direction = direction.
Example: a cart pulled $15\,\text{N}$ to the right and $20\,\text{N}$ to the left yields a net of $5\,\text{N}$ to the left.

For a non-accelerating object: $\sum F = 0$ (equivalently $F_{net} = 0$ ).
Example: standing on two scales with weight evenly distributed; each scale reads half your weight.

Mass: amount of matter; fundamental measure of inertia; independent of gravity.
Weight: gravitational force; $W = mg$ .
Mass is the same on Earth and Moon; weight varies with gravity.
1 kilogram ≈ $10\,\text{N}$ ; 1 kg ≈ $2.2\,\text{lb}$ ; 1 lb ≈ $4.45\,\text{N}$ .

Free fall (negligible air): acceleration ≈ $g \approx 9.8\ \mathrm{m/s^2}$ ; all objects fall with the same acceleration.
Nonfree fall: air resistance depends on speed and frontal area.
Terminal velocity: when $F_{air} = W$ ; net force is zero; velocity becomes constant.
Coin and feather: in air, coin lands first; in vacuum, they fall together.

Acceleration is proportional to net force: $a = \frac{F_{net}}{m}$ .
Greater mass → greater inertia; for the same net force, acceleration is smaller.

Friction depends on materials and contact force; arises from surface roughness and stickiness; opposes motion.

For every action there is an equal and opposite reaction; action–reaction pairs act on different objects.
Examples: rocket and exhaust; wings deflect air to produce lift.