AP Physics 2 Equation & Formula Sheet 2027

A gas exerts 600 N perpendicular to a 0.020 m² wall, so P = 30 kPa.

At the same temperature, lighter particles have a larger rms speed even though average translational kinetic energy is the same.

Heating a gas shifts the distribution toward higher speeds and spreads it over a wider range.

For fixed n and T, doubling V halves P.

A sealed flexible gas sample can be compared before and after simultaneous compression and heating.

At fixed V, a P-versus-T(K) graph is linear and extrapolates toward zero pressure at zero kelvin in the ideal model.

A hot metal block placed in cooler water transfers energy to the water until their temperatures approach one another.

Two samples can still exchange microscopic energy in both directions at equilibrium, but there is no net transfer.

A hot cup loses energy by conduction through the cup, convection to moving air and thermal radiation to the surroundings.

For a fixed amount of ideal monatomic gas, doubling T doubles U.

A compressed gas can gain internal energy even if no heating occurs because W_on is positive.

Expansion has ΔV>0 so W_on<0; compression has ΔV<0 so W_on>0.

For the same Q and m, a material with larger c undergoes a smaller temperature change.

Doubling insulation thickness halves the ideal steady conduction rate when other quantities remain fixed.

A high-k metal transfers energy faster than a low-k insulating material of the same size under the same temperature difference.

A hot object and a cold object inside an insulated enclosure spontaneously approach one common temperature; total entropy increases.

An ideal reversible limit can connect equilibrium states without increasing total entropy.

A gas freely expanding into an evacuated region spreads into more accessible configurations and increases total entropy.

If the separation doubles while charges and medium stay fixed, the force magnitude becomes one fourth as large.

An object with 5×10⁶ excess electrons has q=−5×10⁶e.

For three charges, determine each force direction first and add components rather than adding magnitudes.

If electrons enter an initially neutral isolated metal object, its final net charge is negative by exactly the transferred amount.

Rubbing two initially neutral objects can leave equal-and-opposite net charges while the two-object total remains zero.

A charged rod brought near a neutral conductor can attract the conductor even before contact because mobile charge separates.

A 2.0 μC positive test charge experiencing 0.060 N to the right is in a field of 3.0×10⁴ N/C to the right.

Doubling distance from an isolated point charge reduces field magnitude by a factor of four.

Between equal unlike charges, the two field contributions at the midpoint point in the same direction and therefore add.

Like charges give positive U_E at finite separation; opposite charges give negative U_E with this reference.

For three charges, include the 1–2, 1–3 and 2–3 pair energies once each.

External work is positive when like charges are slowly brought closer from very far apart.

If a +2 C test charge would have 6 J of electric potential energy at a point, that point is at 3 V.

A positive and negative source can give zero potential at a point even when the electric field there is not zero.

Moving in the electric-field direction lowers electric potential; closely spaced equipotentials indicate a stronger field.

For a fixed capacitor, doubling Q doubles |ΔV|; C itself does not change.

Increasing plate area raises C; increasing separation lowers C; inserting a dielectric raises C and reduces the field for fixed free plate charge.

At fixed C, doubling voltage quadruples stored energy; at fixed Q, increasing C lowers stored energy.

A positive charge moving to lower potential has ΔU_E<0; a negative charge has the opposite sign relation.

A released positive charge moving to lower potential gains kinetic energy equal to the electric potential-energy decrease.

An electron accelerated through a potential difference can be analyzed by the same energy bookkeeping once the charge sign is handled correctly.

6 C crossing in 3 s corresponds to 2 A

0.50 A for 8 s transfers 4 C

an open circuit can contain moving electrons microscopically while having zero net charge flow

closing a switch completes the loop and allows current

an open switch prevents current in its branch

a wire placed across an element can bypass that element

doubling length doubles resistance; doubling area halves resistance

a 4 Ω resistor carrying 2 A has 8 V across it

always read axis labels before converting graph slope into resistance

12 V across a device carrying 2 A corresponds to 24 W

at fixed current, doubling R doubles power

at fixed voltage, doubling R halves power

3 Ω and 5 Ω in series give 8 Ω

two identical resistors in parallel have half the resistance of either one

reduce valid subgroups first, then determine total source current

source rises and resistor drops sum to zero

a positive charge gains electric potential energy when it moves through a potential rise

all points on one ideal-wire node share the same potential

3 A entering and 1 A leaving one branch requires 2 A to leave through the remaining branch

take entering currents positive and leaving currents negative, or vice versa

source current equals the sum of parallel-branch currents

series equivalent capacitance is smaller than the smallest individual capacitance

parallel capacitances add directly

after one time constant charging reaches about 63% of final charge while discharging retains about 37% of its initial charge

outside a bar magnet the field points away from the north pole and toward the south pole, then continues through the magnet

a ferromagnetic sample can retain substantial alignment after an external field is removed, whereas a paramagnetic sample does not

the long-straight-wire field model in Topic 12.3 uses μ₀

for v perpendicular to B, F_B=|q|vB; for v parallel or antiparallel to B, F_B=0

doubling speed doubles the radius while doubling B halves the radius

in perpendicular crossed fields, equal and opposite electric and magnetic forces can transmit a selected particle speed

doubling I doubles B; doubling r halves B

a wire perpendicular to B experiences maximum force; a parallel wire experiences zero force

fields in opposite directions subtract in magnitude, while fields in the same direction add

flux is maximum in magnitude when B is parallel to the area vector and zero when B lies in the surface plane

doubling the flux change in the same time doubles the emf magnitude

doubling rod speed doubles the motional emf

a ray arriving 35° from the normal leaves 35° from the normal on the other side

parallel planar wavefronts correspond to parallel light rays normal to those wavefronts

paper can look bright from many viewing directions because different microscopic patches have different normals

a concave mirror with an object beyond its focal point can produce a positive real-image distance

negative M represents an inverted image under the stated sign convention

a concave spherical mirror with R=40 cm has |f|=20 cm

larger n corresponds to smaller light speed v

air-to-glass transmission bends toward the normal because n increases

for glass-to-air, incidence greater than θ_c produces total internal reflection

a converging lens with an object beyond f can form a real image on the transmitted side

negative magnification corresponds to an inverted real image under the stated convention

two correctly drawn principal rays are sufficient to locate an image, while a third provides a consistency check

increasing tension raises wave speed; increasing linear density lowers it

a 0.020 kg string 2.0 m long has μ=0.010 kg/m

a larger-amplitude sound wave is associated with greater intensity/loudness than an otherwise similar smaller-amplitude wave

at v=12 m/s and f=4 Hz, λ=3 m

a 50 Hz wave has T=0.020 s

successive crests are separated by one wavelength

the transmitted wavelength can change when speed changes even though frequency does not

6 W distributed across 2 m² corresponds to 3 W/m²

a pulse reflecting where the transmitted-wave speed is lower returns inverted; if transmitted speed is higher, it returns without inversion

higher-frequency electromagnetic radiation has shorter wavelength

if the wave travels in +x and E oscillates along y, B is perpendicular to both

visible light lies between infrared and ultraviolet in the spectrum

an approaching siren is heard at a higher frequency than when there is no relative motion

after the siren passes and moves away, the observed frequency is lower

a faster approach produces a larger upward frequency shift than a slower approach

equal and opposite pulses can momentarily cancel before continuing through each other

440 Hz and 444 Hz produce 4 beats per second

a closed-open air column supports odd quarter-wavelength modes

a narrower slit makes the first minimum occur at a larger angle

increasing screen distance spreads the observed pattern

doubling λ approximately doubles the central-maximum width

longer wavelength produces a larger angle at the same order and spacing

larger slit separation moves neighboring fringes closer together

600 lines/mm corresponds to d≈1.67×10⁻⁶ m

changing thickness changes which wavelengths reinforce or cancel

an oil film can enhance different colors as its thickness varies

a coating can suppress reflection of a chosen wavelength by making the two reflected rays arrive out of phase

a higher-frequency photon carries more energy

a shorter-wavelength photon carries greater momentum

increasing a particle’s momentum decreases its de Broglie wavelength

carbon-14 has Z=6 and therefore Nn=8 neutrons

changing allowed radius changes the electric force and model orbital speed

only circumferences containing an integer number of de Broglie wavelengths satisfy the standing-wave condition

a larger level gap corresponds to a higher-frequency photon

larger energy gaps produce shorter wavelengths

an upward arrow requires photon absorption; a downward arrow corresponds to photon emission

a hotter blackbody peaks at a shorter wavelength

doubling T at fixed A increases P by a factor of 16

at equal area, a 20% temperature increase raises power by (1.2)⁴

at fixed material, increasing frequency raises Kmax linearly

a 2.0 eV maximum kinetic energy corresponds to a 2.0 V stopping-potential magnitude

below f0, raising intensity does not cause emission in the one-photon model

θ=0 gives no Compton wavelength shift; backscatter gives the maximum shift

because λf>λi after an energy-transferring scatter, the photon momentum decreases

a longer scattered wavelength means lower photon energy, with the difference transferred to the electron/system

a small decrease in total rest mass can appear as kinetic energy of products and/or photon energy

a shorter half-life corresponds to a larger decay constant

after three half-lives the expected remaining population is N0/8

the daughter has four fewer nucleons and two fewer protons than the parent

β− raises daughter Z by 1 at fixed A; β+ lowers daughter Z by 1 at fixed A

gamma emission changes nuclear energy but not the element or isotope identity