The core ideas include conservation laws, field models, wave behavior, and energy transfer. Fluid problems often use pressure, buoyancy, continuity, and Bernoulli's equation, while thermodynamics connects heat, work, internal energy, and ideal gases. Electricity and magnetism rely on Coulomb's law, electric potential, capacitance, circuits, magnetic force, and induction.
Optics and modern physics use wave relationships, mirrors and lenses, photon energy, and nuclear or atomic energy changes.
Key Facts
- Fluid pressure is given by , and the pressure at depth in a fluid is .
- The buoyant force on an object equals the weight of displaced fluid, so .
- For ideal fluid flow, the continuity equation is and Bernoulli's equation is .
- The ideal gas law is , and the average translational kinetic energy per molecule is .
- The first law of thermodynamics is , where is heat added to the system and is work done on the system.
- Coulomb's law is , and the electric field from a point charge is .
- Capacitance is , and the energy stored in a capacitor is .
- Photon energy is , and mass-energy equivalence is .
Vocabulary
- Pressure
- Pressure is the force applied perpendicular to a surface per unit area, calculated by .
- Buoyant Force
- Buoyant force is the upward force a fluid exerts on an object equal to the weight of the displaced fluid.
- Electric Field
- An electric field is the force per unit positive test charge at a location, defined by .
- Capacitance
- Capacitance is a measure of how much charge a device stores per potential difference, given by .
- Magnetic Flux
- Magnetic flux measures how much magnetic field passes through an area and is calculated by .
- Photon
- A photon is a packet of electromagnetic energy with energy .
Common Mistakes to Avoid
- Using gauge pressure when absolute pressure is required is wrong because gas laws such as require absolute pressure, not pressure relative to the atmosphere.
- Forgetting that buoyant force depends on displaced fluid volume is wrong because , not the object's total volume unless it is fully submerged.
- Adding resistors and capacitors with the same rules is wrong because series resistors add as , while series capacitors use .
- Ignoring the sign of work in thermodynamics is wrong because depends on whether work is done on the gas or by the gas.
- Treating wavelength as unchanged when light enters a new medium is wrong because frequency stays constant while speed and wavelength change according to .
Practice Questions
- 1 A hydraulic lift has a small piston area of and a large piston area of . If a force of is applied to the small piston, what force is produced on the large piston?
- 2 A capacitor is connected to a battery. Find the charge stored on the capacitor and the energy stored in it.
- 3 A photon has wavelength . Using , calculate its energy in joules.
- 4 A sealed gas container is heated while its volume stays constant. Explain what happens to the gas pressure using the ideal gas law and particle motion.
Understanding AP Physics 2 Formula Sheet
A formula sheet is most useful when you know the model behind each equation. In fluid questions, first decide whether the fluid is still or moving. A lake, a hydraulic lift, and a floating boat usually involve fluid at rest.
A narrowing pipe or a spray nozzle involves flow. Density is often the hidden idea. An object floats when it can displace enough water for the upward fluid force to balance its weight.
In a flow problem, a smaller cross section makes the fluid move faster if the flow rate stays steady. Treat these results carefully because real fluids can have viscosity, turbulence, and energy loss that ideal models ignore.
Thermodynamics problems depend heavily on defining the system. The system might be gas inside a cylinder, water in a cup, or an engine chamber. Track energy crossing the system boundary as heating or work.
The sign of work is a common source of errors. If a gas expands and pushes a piston, it transfers energy outward. If a piston compresses the gas, energy is transferred into it through work.
A pressure and volume graph gives physical meaning to work because the area under a process curve represents energy transferred by the gas. Temperature measures average molecular motion, but it is not the same thing as total thermal energy. A large cool object can contain more internal energy than a small hot object.
Electricity becomes clearer when you separate force, field, potential, and energy. A field describes what a charge would experience at every location. Electric potential describes energy per unit charge, so it is often easier to use for circuit reasoning.
Charges do not have to move from high potential to low potential in every situation. Positive test charges do, while electrons move in the opposite direction. In circuits, current is the rate of charge flow.
A battery provides an energy increase per unit charge, while resistors transfer electrical energy into heating, light, or motion. Capacitors matter in camera flashes, touch screens, and timing circuits because they can store separated charge temporarily.
Magnetic force requires motion or moving charge. It changes the direction of a charged particle, often producing circular motion, but it does no work on the particle when the force stays perpendicular to the motion. This difference helps explain particle accelerators and mass spectrometers.
In optics, draw a diagram before selecting an equation. Mark the principal axis, object position, focal point, and expected image direction. A converging lens can make a real inverted image on a screen, yet it can make a virtual upright image when the object is close.
Modern physics formulas connect wavelength, frequency, and energy. Shorter wavelength light carries more energy per photon. When using any formula sheet, write units first, sketch the situation, identify assumptions, and check whether the final size and direction make physical sense.