PHY 1071: Physics for Biosciences and Geosciences Flashcards

Vocabulary practice cards covering vector calculus, mechanics, and electrostatics concepts as presented in the PHY 1071 exams.

Cartesian Coordinates of Point M

The position of a point in space defined by the triplet $(x, y, z)$, such as $(1, 1, \sqrt{2})$ in the context of cylindrical conversion.

Irrotational Vector

A vector field $\mathbf{V}$ where the curl (rotational) is zero; used to determine constants $(a, b, c)$ in the function $\mathbf{V} = (x + 2y + az)\mathbf{i} + (bx - 3y - z)\mathbf{j} + (4x + cy + 2z)\mathbf{k}$.

Divergence

A scalar operator $\mathbf{\nabla} \cdot \mathbf{f}$; for the function $\mathbf{f}(x, y, z) = (2x)^2\mathbf{i} + (xyz - y^3)\mathbf{j} - (5x + yz)\mathbf{k}$, it is evaluated at the specific point $(2, 3, 6)$.

Curl (Rotational)

A vector operator acting on a vector field $\mathbf{F}$, denoted as $\text{rot } \mathbf{F}$ or $\mathbf{\nabla} \times \mathbf{F}$, which measures the rotation at a point like $(0, 2, 1)$.

Work ($W$)

The energy transferred by a force field along a curve $(c)$, calculated as $W = \int_c \mathbf{F} \cdot d\mathbf{r}$. In the notes, it is calculated for $\mathbf{F} = 3xy\mathbf{i} - y\mathbf{j}$ along $y = 3x^2$.

Kinetic Energy ($E_c$)

The energy of a particle of mass $m$ in motion, defined as $E_c = \frac{1}{2} m v^2$. In the transcript, it is calculated for a mass $m = 80\,g$ at time $t = 2\,s$.

Magnitude of Acceleration

The scalar value of the acceleration vector $\mathbf{a} = \frac{d^2 \mathbf{r}}{dt^2}$. For parametric equations $x = 2e^{-3t}$, $y = 4\sin(3t)$, and $z = 5\cos(3t)$, it is evaluated at $t = 0$.

Conservative Force

A force $\mathbf{F}$ that can be derived from a scalar potential $E_p$ ($\mathbf{F} = -\mathbf{\nabla} E_p$), requiring its curl to be zero.

Coulomb's Constant ($k$)

A proportionality constant used in electrostatics, given in the transcript as $k = 9 \times 10^9\,SI$.

Electrostatic Force

The force between two charges $q_A$ and $q_B$. In the notes, $q_A = 10^{-6}\,C$ and $q_B = -4q_A$, located at specific cartesian points.

Scalar Product (Dot Product)

An algebraic operation that takes two equal-length sequences of numbers and returns a single number, used to find the angle between vectors like $\mathbf{A}$ and $\mathbf{B}$.

Unit Vector ($\mathbf{u}$)

A vector with a magnitude of exactly $1$, often denoted as $\mathbf{u} = \frac{\mathbf{U}}{|\mathbf{U}|}$.

Gradient ($\text{grad } f$)

A vector operator denoted as $\mathbf{\nabla} f$ that points in the direction of the greatest rate of increase of a scalar function, such as $f(x, y, z) = e^x \cos(2yz)$.

Magnitude of Velocity

The norm of the velocity vector $\mathbf{v} = \frac{d \mathbf{OM}}{dt}$. Calculations in the notes use the position vector $\mathbf{OM} = (-3t^2 + 2t)\mathbf{i} + 5t\mathbf{j} + (4t^3 - 3t)\mathbf{k}$ at $t = 2$.