Classical Physics Comprehensive Exam Flashcards

Comprehensive vocabulary flashcards covering the full curriculum of a classical physics lecture series, from mechanics and thermodynamics to modern physics and relativity.

Right-handed coordinate system

A convention for x, y, and z axes where curling right-hand fingers from positive x toward positive y results in the thumb pointing toward positive z, ensuring consistent cross products like $\hat{x} \times \hat{y} = \hat{z}$.

Cartesian coordinates

A rectilinear system specifying points by perpendicular distances (x, y, z) from a fixed origin, ideal for rectangular geometries.

Polar coordinates

A curvilinear 2D system describing a point by its radial distance $r$ from the origin and the angle $\theta$ from the positive x-axis.

Scalar quantity

A quantity described by a single real number and a unit, possessing magnitude but no direction, such as mass or temperature.

Vector quantity

A quantity requiring both magnitude and direction for complete specification, such as velocity or force.

Dot product (scalar product)

A vector operation result in a scalar defined as $\mathbf{A} \cdot \mathbf{B} = |A||B|\cos(\theta)$, representing the projection of one vector onto another.

Cross product (vector product)

A vector operation resulting in a vector perpendicular to both inputs, defined as $\mathbf{A} \times \mathbf{B} = |A||B|\sin(\theta) \mathbf{\hat{n}}$.

Instantaneous velocity

The limit of average velocity as the time interval reaches zero, mathematically defined as the derivative of position: $\mathbf{v}(t) = \frac{d\mathbf{r}}{dt}$.

Instantaneous acceleration

The limit of average acceleration as the time interval reaches zero, defined as $\mathbf{a}(t) = \frac{d\mathbf{v}}{dt} = \frac{d^2\mathbf{r}}{dt^2}$.

Unit vector

A dimensionless vector with a magnitude of exactly $1$ used to specify a direction, such as $\mathbf{\hat{x}}$, $\mathbf{\hat{y}}$, and $\mathbf{\hat{z}}$ in Cartesian space.

Inertial reference frame

A non-accelerating coordinate system in which Newton's First Law holds true.

Uniform circular motion

Motion along a circular path at constant speed, resulting in a continuously changing velocity direction and a center-seeking acceleration.

Centripetal acceleration

Acceleration directed toward the center of a circular path, with magnitude $a_c = \frac{v^2}{r} = \omega^2 r$.

Radian

The SI unit of angle defined as the ratio of arc length to radius ($\theta = \frac{s}{r}$), where one full revolution equals $2\pi$ rad.

Non-contact forces (field forces)

Forces that act over a distance mediated by fields, such as gravity, electrostatics, and magnetism.

Newton's First Law (Inertia)

An object at rest remains at rest and an object in motion continues at constant velocity unless acted upon by a net external force.

Newton's Second Law

The net force on an object equals the rate of change of its linear momentum, or $\sum \mathbf{F} = m\mathbf{a}$ for constant mass.

Newton's Third Law

For every action force, there is an equal and opposite reaction force acting simultaneously on a different object.

Inertia

The intrinsic tendency of matter to resist changes in its state of motion, quantitatively measured by inertial mass.

Normal force

The contact force exerted by a surface perpendicular to itself, arising from electromagnetic repulsion between atoms at the interface.

Atwood's machine

A device with two masses connected by a string over a pulley, used to study uniform acceleration with the formula $a = \frac{(m_2 - m_1)g}{m_1 + m_2}$.

Static friction ($f_s$)

A reactive contact force that prevents surfaces from sliding, reaching a maximum of $f_{s,max} = \mu_s N$.

Kinetic friction ($f_k$)

A contact force opposing relative motion between sliding surfaces, equal to $f_k = \mu_k N$, where $\mu_k < \mu_s$.

Normal (Gaussian) distribution

A symmetric bell-shaped probability distribution defined by mean $\mu$ and standard deviation $\sigma$, following the 68-95-99.7 rule.

Extrapolation

The process of estimating a function's value at a point outside the range of measured data, assuming the established trend continues.

Least squares method

A mathematical technique to find the best-fit model for data by minimizing the sum of the squares of the residuals (errors).

Centrifugal force

A fictitious (pseudo) force in a rotating reference frame directed radially outward from the axis of rotation.

Conical pendulum

A pendulum bob revolving in a horizontal circle such that the string traces a cone, where the period is $T = 2\pi \sqrt{\frac{L\cos(\theta)}{g}}$..

Banked curve

A roadway tilted toward the center of a curve to provide an inward component of the normal force to assist centripetal acceleration.

Drag force

A resistive force from a fluid directed opposite to motion, often defined as $F_{drag} = \frac{1}{2} \rho C_d A v^2$ for high-speed flows.

Terminal velocity

The constant speed reached by a falling object when the upward drag force equals the downward force of gravity ($v_t = \sqrt{\frac{2mg}{\rho C_d A}}$).

Universal Gravitation

Newton's law stating every particle attracts every other particle with a force $F = \frac{G m_1 m_2}{r^2}$, where $G = 6.674 \times 10^{-11} N \cdot m^2/kg^2$.

Shell Theorem

A theorem stating a uniform spherical mass attracts external objects as if all its mass were at its center and exerts zero net gravitational force on objects inside.

Geostationary orbit

A circular equatorial orbit with a period of 24 hours, keeping a satellite above a fixed point on Earth at approximately $35,786$ km altitude.

Weightlessness

The condition of microgravity experienced in free fall, where no normal contact forces are present despite the presence of gravity.

Kepler's Second Law

A line joining a planet and the Sun sweeps out equal areas in equal time intervals due to conservation of angular momentum.

Kepler's Third Law (Harmonic Law)

The square of a planet's orbital period is proportional to the cube of its semi-major axis: $T^2 \propto a^3$.

Lagrange Point L1

An unstable equilibrium point between two primary masses where the gravitational and centrifugal forces on a smaller object balance.

Gauss's Law for Gravity

An integral law stating the gravitational flux through a closed surface is proportional to the enclosed mass: $\oint \mathbf{g} \cdot d\mathbf{A} = -4\pi G M_{enc}$.

Work

The scalar energy transfer to an object by a force acting over a displacement, defined as $W = \mathbf{F} \cdot \mathbf{d} = |F||d|\cos(\theta)$ for constant force.

Hooke's Law

The linear relationship for springs stating the restoring force is proportional and opposite to displacement: $F_s = -kx$.

Kinetic Energy ($KE$)

The energy of an object due to its motion, defined as $KE = \frac{1}{2} m v^2$ for translation.

Work-Energy Theorem

The net work done on a particle equals the change in its kinetic energy: $W_{net} = \Delta KE$.

Gravitational potential energy ($U_{grav}$)

The energy stored based on position in a gravitational field, given as $mgh$ near Earth or $-\frac{GMm}{r}$ for large distances.

Elastic potential energy ($U_{elastic}$)

The energy stored in a deformed elastic object, defined for a spring as $U = \frac{1}{2} k x^2$.

Conservative force

A force where the work done between two points is path-independent and the work around a closed loop is zero, such as gravity or spring forces.

Mechanical energy

The sum of the kinetic and potential energies of a system ($E_{mech} = KE + U$).

Escape velocity

The minimum speed required for an object at the surface of a planet to escape its gravitational pull, defined as $v_{esc} = \sqrt{\frac{2GM}{R}}$.

Power

The rate at which energy is transferred or work is done, measured in Watts ($W = J/s$) and defined as $P = \frac{dW}{dt} = \mathbf{F} \cdot \mathbf{v}$.

Linear momentum ($\mathbf{p}$)

A vector quantity defined as the product of an object's mass and velocity: $\mathbf{p} = m\mathbf{v}$.

Elastic collision

A collision where both the total linear momentum and total kinetic energy of the system are conserved.

Perfectly inelastic collision

A collision where momentum is conserved but the maximum possible kinetic energy is lost as the objects stick together.

Tsiolkovsky Rocket Equation

An equation relating rocket velocity change to exhaust velocity and the ratio of initial to final mass: $\Delta v = v_e \ln\left(\frac{M_0}{M_f}\right)$.

Impulse (\mathbf{J})

The integral of force over time, equal to the change in an object's linear momentum: $\mathbf{J} = \int \mathbf{F} dt = \Delta \mathbf{p}$.

Ballistic pendulum

A device used to measure bullet speed using momentum conservation during the inelastic collision and energy conservation during the subsequent swing.

Center of mass (CM)

The unique point representing the average position of all the mass in a system, which moves as if all external forces were applied there.

Angular velocity ($\omega$)

The rate of change of angular position, measured in rad/s: $\omega = \frac{d\theta}{dt}$.

Torque (\mathbf{\tau})

The rotational analog of force measuring the tendency to cause rotation, defined as $\mathbf{\tau} = \mathbf{r} \times \mathbf{F}$.

Moment of inertia ($I$)

The measure of an object's resistance to angular acceleration, defined for a collection of particles as $\sum m_i r_i^2$.

Parallel Axis Theorem

A theorem used to find the moment of inertia about any axis parallel to one through the center of mass: $I = I_{cm} + Md^2$.

Rolling without slipping

A condition linking translation and rotation where the contact point is at rest relative to the surface ($v_{cm} = R\omega$).

Angular momentum (\mathbf{L})

The rotational analog of linear momentum, defined for a rigid body as $\mathbf{L} = I\mathbf{\omega}$ and for a point mass as $\mathbf{r} \times \mathbf{p}$.

Fictitious forces

Apparent forces in non-inertial frames such as centrifugal, Coriolis, and Euler forces, which are proportional to the object's mass.

Coriolis force

A fictitious force in a rotating frame acting on a moving object, given by $\mathbf{F}_c = -2m(\mathbf{\Omega} \times \mathbf{v}')$, causing deflections in paths.

Static equilibrium

A state where both the net external force and net external torque on a rigid body are zero ($\sum \mathbf{F} = 0$ and $\sum \mathbf{\tau} = 0$).

Young's Modulus ($E$)

The measure of a material's stiffness under tension or compression, defined as the ratio of tensile stress to longitudinal strain: $E = \frac{F/A}{\Delta L/L}$.

Bulk Modulus ($B$)

The measure of a material's resistance to uniform compression, defined as $B = -V \frac{dP}{dV}$.

Pascal's Principle

A pressure change applied to an enclosed static fluid is transmitted undiminished to every point in the fluid and the container walls.

Archimedes' Principle

The upward buoyant force on an object submerged in a fluid equals the weight of the fluid it displaces ($F_B = \rho_{fluid} V_{disp} g$).

Viscosity ($\eta$)

The measure of a fluid's internal resistance to flow (friction between layers), typically decreasing with temperature in liquids and increasing in gases.

Equation of Continuity

A statement of mass conservation for fluids: $\rho_1 A_1 v_1 = \rho_2 A_2 v_2$, which for incompressible fluids simplifies to $A_1 v_1 = A_2 v_2$.

Bernoulli's Equation

Conservation of energy for an ideal fluid along a streamline: $P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$.

Torricelli's Theorem

The speed of fluid exiting a small hole at depth $h$ from a large tank is $v = \sqrt{2gh}$, equivalent to free-fall speed.

Magnus effect

The generation of a sideward force on a spinning object moving through air due to pressure differences created by asymmetric airflow.

Surface tension (\gamma)

The force per unit length trying to minimize a liquid's surface area due to unbalanced cohesive forces at the interface.

Capillary action

The spontaneous rise or fall of a liquid in a narrow tube driven by the competition between adhesion and cohesion.

Brownian motion

The random jiggling of microscopic particles in a fluid caused by unbalanced molecular bombardment, providing proof of atoms.

Wien's Displacement Law

The blackbody law stating the wavelength of maximum emission is inversely proportional to absolute temperature: $\lambda_{max} T = 2.898 \times 10^{-3} m \cdot K$.

Stefan-Boltzmann Law

The law stating the total power radiated by a blackbody is proportional to the fourth power of its absolute temperature: $P = \sigma A T^4$.

Ideal gas

A theoretical gas consisting of point-like molecules with zero volume that undergo perfectly elastic collisions and have no intermolecular forces.

Kinetic theory of gases

A framework relating macroscopic properties like pressure and temperature to microscopic molecular motion, showing $\text{avg } KE = \frac{3}{2} k_B T$.

Maxwell-Boltzmann distribution

A probability distribution characterizing the speeds of molecules in a gas at a specific temperature.

Triple point

The specific temperature and pressure at which the solid, liquid, and gas phases of a substance coexist in equilibrium.

Fick's First Law

The principle that diffusion flux is proportional to the negative concentration gradient: $J = -D \frac{dC}{dx}$.

Conduction

Heat transfer via direct molecular interaction without bulk matter motion, governed by Fourier's Law ($\frac{dQ}{dt} = -kA \frac{dT}{dx}$).

Specific heat capacity ($c$)

The amount of heat required to raise the temperature of 1 kg of a substance by 1 K without a phase change ($Q = mc\Delta T$).

Latent heat ($L$)

The heat required per unit mass to change the phase of a substance at constant temperature ($Q = mL$).

Internal energy ($U$)

The total microscopic energy of a system, including all molecular kinetic and potential energies, depending only on temperature for ideal gases.

Zeroth Law of Thermodynamics

A fundamental law stating that if two systems are each in thermal equilibrium with a third, they are in equilibrium with each other, defining temperature.

First Law of Thermodynamics

The conservation of energy for thermodynamic systems: $\Delta U = Q - W$, where $Q$ is heat added and $W$ is work done by the system.

Second Law of Thermodynamics

The law stating the total entropy of an isolated system never decreases, defining the direction of spontaneous processes.

Entropy ($S$)

A state function quantifying disorder or microscopic configurations, defined as $dS = \frac{\delta Q_{rev}}{T}$ or $S = k_B \ln(\Omega)$.

Carnot efficiency

The maximum possible efficiency for a heat engine operating between two temperatures: $\eta = 1 - \frac{T_C}{T_H}$..

Equipartition theorem

The principle that each active quadratic degree of freedom in a molecules contributes $\frac{1}{2} k_B T$ to the internal energy.

Simple Harmonic Motion (SHM)

Periodic oscillation where the restoring force is directly proportional to displacement ($F = -kx$), resulting in sinusoidal motion.

Damped oscillations

Oscillatory motion where a dissipative force like friction causes the amplitude to decay exponentially over time.

Resonance

The phenomenon where a system oscillates with maximum amplitude when driven at its natural frequency.

Transverse wave

A wave where the medium oscillates perpendicular to the direction of energy propagation, such as waves on a string or light.

Longitudinal wave

A wave where the medium oscillates parallel to the direction of propagation, such as sound waves.

Principle of Superposition

The rule that the resultant displacement of two overlapping waves is the algebraic sum of their individual displacements.