Units, Physical Quantities, and Vectors

A comprehensive collection of vocabulary flashcards covering SI units, measurement uncertainty, Fermi questions, and vector operations based on physics lecture notes.

SI

The metric system of units, short for Système International.

Meter

The unit of length in the metric system, defined as the distance that light travels in vacuum in a time interval of $(1 / 299,792,457)\,\text{seconds}$.

Kilogram

The unit of mass in the metric system, represented by the mass of a particular cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures near Paris, France.

Second

The unit of time in the metric system, defined as the time required for $9,192,631,770$ cycles of a particular microwave radiation causing cesium atoms to undergo a transition between their two lowest energy states.

mks system

Another name for the metric system of units, standing for meter, kilogram, and second.

Fermi Questions

Questions designed so that reasonable assumptions linked with simple calculations can narrow down the range of values within which an answer must lie.

Order of Magnitude

The power of $10$ of the number that fits a specific physical value; to increase by this means to increase by a power of $10$.

Error

A term for uncertainty used when a value is not known precisely; it represents uncertainty and is distinct from mistakes or sloppiness.

Significant figure

A reliably known digit in a numerical value.

Scalar quantity

A physical quantity that has magnitude only, such as mass, time, temperature, volume, density, energy, distance, speed, and electric charge.

Vector quantity

A physical quantity that has both magnitude and direction, such as displacement, velocity, acceleration, force, linear momentum, angular momentum, electric field, magnetic field, and torque.

Displacement vector

A vector whose magnitude is the shortest distance between the initial and final positions of an object, with a direction pointing from the initial position to the final position.

Commutative

A property of vector addition meaning that the order in which vectors are added does not matter: $A + B = B + A$.

Components of a vector

The projections of a vector along the axes of a rectangular coordinate system, denoted as $A_x$ and $A_y$.

Unit vector

A vector of magnitude one, used to indicate direction along an axis, such as the positive x-axis, y-axis, or z-axis.

Scalar (Dot) Product

A multiplication of two vectors resulting in a scalar, calculated using the formula $A \cdot B = |A| |B| \cos(\phi)$, where $\phi$ is the smallest angle between them.

Vector (cross) Product

A multiplication of two vectors resulting in a third vector $C = A \times B$ that is perpendicular to both original vectors, with a magnitude given by $|C| = |A| |B| \sin(\phi)$.

Right-hand-rule

A method to determine the direction of a cross product by pointing the fingers of the right hand in the direction of the first vector and aiming the palm toward the second; the thumb then points in the direction of the result.