MCAT Physics Syllabus

State Pascal's principle.

A pressure change applied to an enclosed incompressible fluid is transmitted undiminished to every point in the fluid. This underlies hydraulic systems: $\frac{F_{1}}{A_{1}} = \frac{F_{2}}{A_{2}}$.

State Archimedes' principle and the buoyant force formula.

A body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced: $F_{B} = \rho_{fluid}\, V_{displaced}\, g$.

Define stress and strain, and state Young's modulus.

Stress = force per area $\sigma = \frac{F}{A}$; strain = fractional deformation $\varepsilon = \frac{\Delta L}{L_{0}}$. Young's modulus $Y = \frac{\sigma}{\varepsilon} = \frac{F/A}{\Delta L/L_{0}}$, describing resistance to tensile/compressive deformation.

State Hooke's law for a spring and identify each term.

$F = -kx$, where $F$ is the restoring force, $k$ is the spring constant (stiffness), and $x$ is the displacement from equilibrium. The negative sign shows the force opposes displacement.

State the continuity equation for an ideal fluid.

For an incompressible fluid, volume flow rate is constant: $A_{1}v_{1} = A_{2}v_{2}$. Narrower cross-sections produce higher flow speeds.

State Bernoulli's equation.

$P + \frac{1}{2}\rho v^{2} + \rho g y = \text{constant}$ along a streamline, expressing conservation of energy per unit volume for an ideal fluid.

Define the Reynolds number and its significance.

$Re = \frac{\rho v D}{\eta}$, a dimensionless ratio of inertial to viscous forces. Low $Re$ indicates laminar flow; high $Re$ (typically $> 2000$–$4000$ in pipes) indicates turbulent flow.

State Coulomb's law for the force between two point charges.

$F = k\frac{|q_{1}q_{2}|}{r^{2}}$, where $k \approx 8.99\times10^{9}\ \text{N·m}^{2}/\text{C}^{2}$. The force is attractive for opposite charges and repulsive for like charges.

Define the electric field and give the field of a point charge.

Electric field is force per unit positive test charge: $\vec{E} = \frac{\vec{F}}{q}$. For a point charge: $E = k\frac{|Q|}{r^{2}}$, pointing away from positive and toward negative charge.

Relate electric potential energy and electric potential for point charges.

Potential energy: $U = k\frac{q_{1}q_{2}}{r}$. Electric potential (per unit charge): $V = k\frac{Q}{r}$, so $U = qV$. Potential is a scalar.

State Ohm's law and the formula for electrical power dissipated.

Ohm's law: $V = IR$. Power dissipated: $P = IV = I^{2}R = \frac{V^{2}}{R}$.

How do resistors combine in series versus parallel?

Series: $R_{eq} = R_{1} + R_{2} + \cdots$. Parallel: $\frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \cdots$, so the parallel equivalent is always smaller than the smallest resistor.

How do capacitors combine in series versus parallel, and what is stored energy?

Series: $\frac{1}{C_{eq}} = \sum \frac{1}{C_{i}}$. Parallel: $C_{eq} = \sum C_{i}$. Energy stored: $U = \frac{1}{2}CV^{2} = \frac{Q^{2}}{2C}$. Capacitance: $C = \frac{Q}{V}$.

State Kirchhoff's two circuit laws.

Junction (current) rule: $\sum I_{in} = \sum I_{out}$ (charge conservation). Loop (voltage) rule: the sum of potential changes around any closed loop is zero, $\sum \Delta V = 0$ (energy conservation).

Give the magnetic force on a moving charge and on a current-carrying wire.

On a charge: $\vec{F} = q\vec{v}\times\vec{B}$, magnitude $F = qvB\sin\theta$. On a wire: $\vec{F} = I\vec{L}\times\vec{B}$, magnitude $F = BIL\sin\theta$.

What is the magnetic field magnitude at distance $r$ from a long straight current-carrying wire?

$B = \frac{\mu_{0}I}{2\pi r}$, where $\mu_{0} = 4\pi\times10^{-7}\ \text{T·m/A}$. Field lines form concentric circles given by the right-hand rule.

State Faraday's law of electromagnetic induction.

The induced EMF equals the negative rate of change of magnetic flux: $\varepsilon = -N\frac{d\Phi_{B}}{dt}$, where flux $\Phi_{B} = BA\cos\theta$.

State Lenz's law.

An induced current flows in the direction that opposes the change in magnetic flux producing it. This is the source of the negative sign in Faraday's law and reflects energy conservation.

Relate wave speed, frequency, and wavelength; define period.

$v = f\lambda$. Period is the time for one cycle: $T = \frac{1}{f}$. Frequency $f$ is measured in hertz (cycles per second).

Compare transverse and longitudinal waves with examples.

In transverse waves the oscillation is perpendicular to propagation (e.g., light, waves on a string). In longitudinal waves the oscillation is parallel to propagation (e.g., sound, compression waves).

What are the resonant frequencies of a string (or pipe open at both ends) of length $L$?

$f_{n} = \frac{nv}{2L}$ for $n = 1, 2, 3, \ldots$, where $n=1$ is the fundamental. Harmonics are integer multiples of the fundamental.

Give the resonant frequencies of a pipe closed at one end.

$f_{n} = \frac{nv}{4L}$ for odd $n = 1, 3, 5, \ldots$ only. Even harmonics are absent because of the fixed-end/open-end boundary conditions.

State the equation for the Doppler effect in sound.

$f' = f\left(\frac{v \pm v_{observer}}{v \mp v_{source}}\right)$. Signs are chosen so that relative approach raises the observed frequency and recession lowers it.

Define sound intensity level in decibels.

$\beta = 10\log_{10}\left(\frac{I}{I_{0}}\right)$ dB, where $I_{0} = 10^{-12}\ \text{W/m}^{2}$ is the threshold of hearing. Intensity itself falls off as $I \propto \frac{1}{r^{2}}$.

State the law of reflection and Snell's law of refraction.

Reflection: angle of incidence equals angle of reflection, $\theta_{i} = \theta_{r}$. Refraction (Snell's law): $n_{1}\sin\theta_{1} = n_{2}\sin\theta_{2}$, with index $n = \frac{c}{v}$.

State the thin-lens/mirror equation and the magnification formula.

$\frac{1}{f} = \frac{1}{d_{o}} + \frac{1}{d_{i}}$. Magnification: $m = \frac{h_{i}}{h_{o}} = -\frac{d_{i}}{d_{o}}$. Positive $m$ is upright; negative $m$ is inverted.

Define the critical angle for total internal reflection.

Total internal reflection occurs when light travels from a denser to a rarer medium ($n_{1} > n_{2}$) at angles beyond $\theta_{c}$, where $\sin\theta_{c} = \frac{n_{2}}{n_{1}}$.

State the double-slit condition for constructive interference of light.

Bright fringes (constructive interference) occur when the path difference equals an integer number of wavelengths: $d\sin\theta = m\lambda$, $m = 0, 1, 2, \ldots$. Destructive: $d\sin\theta = (m+\tfrac{1}{2})\lambda$.

State the first law of thermodynamics.

$\Delta U = Q - W$, where $\Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $W$ is work done by the system. It expresses energy conservation.

State the second law of thermodynamics and define entropy change.

The total entropy of an isolated system never decreases: $\Delta S_{universe} \geq 0$. For a reversible process, $\Delta S = \frac{Q_{rev}}{T}$. Heat flows spontaneously from hot to cold.

Give the equations for heat causing temperature change versus phase change.

Temperature change: $Q = mc\Delta T$, where $c$ is specific heat. Phase change (constant temperature): $Q = mL$, where $L$ is the latent heat of fusion or vaporization.