At constant temperature, the pressure and volume of a gas are linked so that their product stays the same as long as the amount of gas remains constant. This is Boyle’s law: PV = constant for a fixed amount of gas when temperature is unchanged. Intuitively, squeezing the gas into a smaller volume forces the molecules to collide with the container walls more often, which raises the pressure. Conversely, allowing the gas to expand lowers the pressure, keeping the product PV constant. The practical implication is that if you compress the gas to half its volume, the pressure roughly doubles to maintain the same PV product, assuming ideal gas behavior. This inverse relationship is what Boyle’s law describes. For broader context, other gas laws describe different relationships: Charles’s law shows V proportional to T at constant pressure, Gay-Lussac’s law shows P proportional to T at constant volume, and Avogadro’s law shows V proportional to the number of particles at constant T and P.

Conservation of angular momentum explains why a spinning gyroscope resists changes in orientation. When a gyroscope spins, it carries angular momentum along its spin axis. If an external torque tries to tilt that axis, the change in angular momentum occurs in a way that causes the axis to precess rather than tilt directly, keeping the orientation relatively stable. In short, the spinning wheel’s angular momentum tends to stay constant unless a torque acts, producing the characteristic precession rather than easy reorientation. The other principles relate to electrical circuits (Ohm’s law), fluid dynamics (Bernoulli), or elasticity (Hooke’s law) and don’t describe gyroscopic stability.

Mach number is the ratio of the aircraft’s true airspeed to the local speed of sound. Since the speed of sound in air depends on temperature, Mach numbers change with altitude because the air temperature changes. At sea level in standard conditions, the speed of sound is about 661 knots, so Mach 1 corresponds to roughly 661 knots true airspeed. As you climb and the air cools, the local speed of sound drops, so Mach 1 equates to a lower TAS in knots—roughly around 570 knots at typical cruise altitudes, depending on the exact temperature profile. This is why Mach 1 isn’t a fixed knot value across altitudes. Ground speed uses the movement over the Earth and is not the Mach calculation, and engine RPM isn’t what Mach number measures.

Hydraulic pumps turn mechanical energy into hydraulic energy by moving fluid. The piston pump fits this role because it uses a piston sliding in a cylinder to trap a fixed amount of fluid and force it out with each stroke, creating flow and pressure. This is the defining feature of a pump: generating flow by displacing fluid. The other items are not pumps. A shuttle valve is a device that selects the higher-pressure source and routes flow, functioning as a valve. A pilot valve is a control valve that uses hydraulic pressure to actuate other components, not a pump. An accumulator stores hydraulic energy by pressing fluid with a gas or spring, but it does not produce flow itself.