General Physics: Units, Vectors, Kinematics, and Dynamics

Vocabulary flashcards defining fundamental physical concepts, vector operations, kinematics, and Newtonian dynamics covered in the lecture notes.

Frame of Reference

A set of coordinates (such as $x, y, z$) used to describe a body or particle's position in space (3D) or in a plane (2D).

Cartesian Coordinate System

The most basic frame of reference in which a particle's position is specified by three spatial coordinates: $x$, $y$, and $z$.

Inertial Frame of Reference

A frame of reference in which Newton's laws and other physical laws hold; an object not acted upon by an outside force remains at rest or moves at a constant velocity in a straight line with zero acceleration.

Non-Inertial Frame of Reference

A frame of reference in which Newton's laws and other physical laws are not valid, defined as a frame that is in a state of acceleration relative to an inertial frame of reference.

Space

A continuous, free, and unoccupied expanse representing the boundless three-dimensional extent in which objects and events occur and have relative position and direction.

Coordinate System

A mathematical scheme that describes, determines, or observes the motion of objects within a given reference frame.

Time

The component of a measuring system used to sequence events, quantify the intervals between them, and measure the rate of change of motion.

Event

An occurrence to which an observer can assign three spatial coordinates and one temporal coordinate, expressed as $(x, y, z, t)$.

Fundamental Units

Standard SI units of measurement that are not derived from or based on other units, including the metre ($\text{m}$), second ($\text{s}$), kilogram ($\text{kg}$), kelvin ($\text{K}$), ampere ($\text{A}$), mole ($\text{mol}$), and candela ($\text{cd}$).

Derived Units

Units formed by algebraic combinations of fundamental units to describe physical quantities, such as area, velocity, density, force, and energy.

Dimensional Homogeneity

The physical condition that requires all terms on both sides of a valid equation to have identical dimensional formulas.

Vector Quantity

A quantity possessing both magnitude and direction, such as displacement, velocity, force, acceleration, and momentum.

Scalar Quantity

A quantity characterized solely by magnitude without an associated spatial direction, such as temperature, volume, speed, distance, and mass.

Unit Vector

A vector that has a magnitude of exactly $1$ and is used to indicate a specific direction in coordinate space.

Parallel Vectors

Two or more vectors that point in the exact same direction, being strictly equal only when both their magnitudes and directions coincide.

Anti-parallel Vectors

Vectors that point in exactly opposite directions along parallel lines, regardless of whether their magnitudes are equal.

Dot Product (Scalar Product)

An algebraic vector multiplication denoted by $\mathbf{A} \cdot \mathbf{B} = AB\cos(\theta)$ that yields a scalar, resulting in zero if the two non-zero vectors are mutually perpendicular (orthogonal).

Cross Product (Vector Product)

A binary vector multiplication denoted by $\mathbf{A} \times \mathbf{B}$ that yields a vector perpendicular to both operands with magnitude $|\mathbf{A} \times \mathbf{B}| = AB\sin(\theta)$, obeying the anticommutative rule $\mathbf{A} \times \mathbf{B} = -(\mathbf{B} \times \mathbf{A})$.

Scalar Triple Product

A composite operation among three vectors defined by $\mathbf{A} \cdot (\mathbf{B} \times \mathbf{C})$ that yields a scalar value equal to the determinant of their coordinate components.

Coplanar Vectors

Vectors that lie in or are parallel to the same plane in three-dimensional space, characterized by their scalar triple product equaling zero ($\mathbf{A} \cdot (\mathbf{B} \times \mathbf{C}) = 0$).

Vector Triple Product

A vector operation defined by $\mathbf{A} \times (\mathbf{B} \times \mathbf{C})$ that results in a vector perpendicular to $\mathbf{A}$ and lying in the plane of $\mathbf{B}$ and $\mathbf{C}$, expandable as $(\mathbf{A} \cdot \mathbf{C})\mathbf{B} - (\mathbf{A} \cdot \mathbf{B})\mathbf{C}$.

Kinematics

The branch of classical mechanics that describes the motion of points, particles, and bodies in terms of position, velocity, and acceleration without considering the forces that cause the motion.

Average Velocity

The ratio of the change in displacement to the elapsed time interval, mathematically defined as $v_{\text{average}} = \frac{\Delta x}{\Delta t}$.

Average Speed

The scalar ratio of the total path length (distance) traveled by an object divided by the total time taken to traverse that distance.

Displacement

The vector difference between the final position and the initial position of a particle along a defined direction ($\Delta x = x_2 - x_1$).

Instantaneous Velocity

The velocity of a particle at a specific instant, evaluated as the limit of the average velocity as the time interval approaches zero ($v = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt}$).

Instantaneous Acceleration

The rate of change of velocity at an infinitesimal instant of time, defined mathematically as $a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} = \frac{dv}{dt}$.

Uniformly Accelerated Motion

Rectilinear motion along a straight line during which acceleration remains constant in magnitude and direction, making average acceleration equal to instantaneous acceleration.

Free Fall

The vertical motion of a body falling near the surface of the Earth under the exclusive influence of Earth's gravity with constant acceleration $g \approx 9.8\,\text{m/s}^2$, in the absence of air resistance.

Trajectory

The parabolic flight path traced through space by an object projected into the air under the influence of gravity.

Range (of a Projectile)

The total horizontal distance traversed by a projectile from its point of projection to the point where it returns to the same elevation, expressed as $R = \frac{v_0^2 \sin(2\theta)}{g}$.

Dynamics

The branch of mechanics that analyzes the motion of bodies and systems while taking into account the forces and causes producing that motion.

Inertia

The property of a body to persist in its state of rest or uniform motion in a straight line unless acted upon by an external net force.

Equilibrium

The mechanical state of a body when the net vector sum of all forces acting upon it equals zero ($\mathbf{F}_{\text{net}} = 0$), causing it to remain at rest or move with a constant velocity.

Normal Force

A contact force exerted perpendicular to the surface of support that counteracts the component of gravitational or applied force pressing an object against that surface.

Weight

The downward gravitational force exerted on an object's mass by gravity, defined mathematically as $W = mg$.

Tension

A pulling force exerted along the length of a flexible medium (such as a string, cable, or rope) by each of its ends.