General Physics I - Space and Time

Space has three independent directions: length, width, and height (or depth).

Space with only one direction to specify a point.

Space that requires two coordinates (like x and y) for a point.

Space requiring three coordinates (x, y, and z) for a point.

A system to describe positions in 3D space using (x, y, z).

A fixed, unchanging space that's the backdrop for events, according to Newton.

Space exists only as relationships between objects, per Leibniz.

Space that isn't perfectly flat; it can curve due to mass and energy.

The ongoing sequence of events from the past to the future.

The four-dimensional continuum including space and time.

The idea that time flows at a constant rate, independent of any observer.

Einstein's concept where the flow of time can vary depending on the observer's speed and gravity field.

The phenomenon where time passes slower for a moving object compared to a stationary one.

The way coordinates are transformed between observers moving at a constant velocity in classical mechanics, assuming time flows at the same rate for all.

A four-dimensional concept that combines space and time into a single entity.

The distance between two events in spacetime, comprising both spatial and temporal differences.

A specific point in spacetime, described by four coordinates (x, y, z, t).

The apparent shortening of an object moving relative to an observer.

A physical constant that relates temperature to the average kinetic energy of particles in a substance.

kg m^2 s^-2 K^-1

Standard units used in the International System of Units (SI) for representing large and small multiples of units.

A measurement of length in micrometers expressed as 10^-6 meters.

A method to check equations and derive relationships based on physical quantity dimensions (like mass, length, and time).

The rate at which velocity changes over time.

A push or pull that can change the motion of an object.

The energy transferred by a force.

The rate at which work is done.

The length of a straight line segment connecting two points in three-dimensional space. Calculated using the distance formula.

The difference in elapsed time between two events as measured by observers moving relative to each other. Proper time is the shortest time interval.

Δt = Δt0/√(1 - v²/c²)

The apparent shortening of an object moving relative to an observer along its direction of motion.

L = L0 √(1 - v²/c²)

International System of Units, based on powers of ten, fundamental units (meter, kilogram, second) and derived units (like velocity).

Independent units in the SI system. Examples include meter for length, kilogram for mass, and second for time.

Units formed from combinations of fundamental units. Examples include velocity (m/s) and volume (m³).

V=γkbT/m

T has dimensions of time, represented as [T].

Radius has dimensions of length, represented as [L].

Density has dimensions of mass per unit volume, represented as [M L-3].

Surface tension has dimensions of force per unit length, represented as [M L0 T-2].

The exponents x, y, and z are determined by equating the dimensions of each quantity in the equation.

To solve the equation T=kaxρyγz dimensionally equate [M], [L], [T], to get three simultaneous equations.

Force is mass times acceleration, and acceleration is the change in velocity over time, resulting in the formula [M L T-2].

Centripetal force is directly proportional to the mass, velocity squared, and inversely proportional to the radius: F ∝ mv²/r.

Determine the dimensions of electrical resistance (R) using known dimensions of other related quantities.