Physics of Motion, Gravity & Energy (Lectures 3, 4 & 5)

Scalar vs. Vector

A scalar is a quantity described by a single number/magnitude (such as mass, temperature, or speed); a vector requires both magnitude and direction (such as velocity, acceleration, or momentum).

Acceleration

The rate of change of velocity; occurs whenever an object speeds up, slows down, or changes direction (such as going around a curve or orbiting a planet).

Acceleration Due to Gravity

All falling objects near a planet's surface accelerate downward at the same rate regardless of how heavy they are, provided air resistance is ignored (demonstrated on the Moon by dropping a hammer and a feather).

Linear Momentum

The product of an object's mass and velocity; an object's momentum can only be changed by an unbalanced net force.

Newton's First Law of Motion

An object moves at constant velocity unless a net force acts to change its speed or direction (motion at constant velocity is the normal state of matter, so a spaceship needs no fuel to keep coasting in space).

Newton's Second Law of Motion

Force equals mass times acceleration; a larger mass has greater inertia(resistance to having its velocity changed) and requires a greater force to achieve the same acceleration.

Newton's Third Law of Motion

For every force, there is always an equal and opposite reaction force acting on the other object (e.g., a rocket expels gas backward to propel itself forward). In a head-on collision between a compact car and a heavy truck, both experience the exact same force and momentum transfer, but the lighter car undergoes a much larger change in velocity.

Mass vs. Weight

Mass is the amount of matter in an object (which stays the same everywhere); weight is the force acting upon that mass due to gravity or acceleration (on the Moon, your mass is the same as on Earth, but your weight is less because the Moon's gravity is weaker).

Free-Fall & Weightlessness [ON EXAM]

You are in free-fall whenever gravity is the ONLY force acting on you; astronauts are weightless in space NOT because there is no gravity, but because they are in a constant state of free-fall as they orbit (fall around) the Earth.

Universal Law of Gravitation

Every mass attracts every other mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers (as distance increases, gravitational attraction weakens rapidly).

Conservation of Energy

Energy makes matter move and cannot be created or destroyed, but it can transfer from one object to another or change in form (all energy traces back to the Big Bang).

Joule vs. Watt

The Joule is the unit used to measure energy; Power is the rate at which energy is used and is measured in Watts (joules per second).

Basic Types of Energy

Kinetic energy (energy of motion), Radiative energy (energy carried by light), and Potential energy (stored energy).

Thermal Energy vs. Temperature

Thermal energy is a sub-type of kinetic energy measuring the total/collectivekinetic energy of all randomly moving particles in a substance (depends on both temperature AND density/number of particles); Temperature is the average kinetic energy of the particles. (Example: Air in a hot oven has a higher temperature due to faster average particle speeds, but a pot of boiling water has greater total thermal energy because water is much denser and has far more molecules).

Kelvin Scale & Absolute Zero

The scientific temperature scale where Absolute Zero represents the coldest possible temperature at which there is no particle motion at all.

Perfect (Ideal) Gas Law

Connects gas pressure, density, and temperature to the average velocity of atoms and molecules; confining a gas to a smaller volume compresses and heats the gas.

Gravitational Potential Energy

Stored energy that depends on an object's mass, the strength of gravity, and the distance the object could potentially fall. When an object falls or a giant gas cloud in space contracts, it trades gravitational potential energy for kinetic/thermal energy (heating up the contracting cloud).

Conservation of Angular Momentum

Because angular momentum must be conserved, as a rotating object or collapsing gas cloud shrinks in radius, it must spin faster (just like a spinning ice skater pulling in her arms).

Mass-Energy

Einstein's discovery that mass itself is a form of potential energy; a tiny amount of mass can release an enormous amount of energy (as in nuclear fission, fusion, or an H-bomb), and concentrated energy can spontaneously turn into particles.

Orbital Energy

The sum of an orbiting object's kinetic energy and gravitational potential energy, which remains constant unless acted on by an outside process. Orbits cannot change spontaneously, but can be altered if an object gains or loses orbital energy through friction (atmospheric drag) or a gravitational encounter (such as a comet passing near Jupiter).

Bound vs. Unbound Orbits

Newton extended Kepler's laws to show that all orbiting objects follow conic sections: bound orbits are ellipses (the object orbits repeatedly), whereas unbound orbits are parabolas or hyperbolas (the object passes by the Sun only once).

Newton's Version of Kepler's Third Law

Generalized Kepler's Third Law to show that if you measure a small orbiting object's orbital period and average orbital distance around a larger object, you can calculate the mass of the larger object (allows astronomers to measure the masses of the Sun, planets with moons, and distant star systems).

Escape Velocity

The speed required for an object to gain enough orbital energy to break free from a bound orbit into an unbound orbit and escape a planet's gravity completely; depends on the mass and radius of the planet, NOT the mass of the escaping object.