PAF GD Pilot Physics Syllabus

Give the formulas for kinetic energy and gravitational potential energy.

Kinetic energy KE = ½mv²; Gravitational potential energy PE = mgh, where h is height above a reference level.

State the law of conservation of energy.

Energy can neither be created nor destroyed, only transformed from one form to another; the total energy of an isolated system remains constant.

Define power and give its formulas and SI unit.

Power is the rate of doing work: P = W/t = F·v. SI unit is the watt (W), where 1 W = 1 J/s. (1 horsepower ≈ 746 W.)

State Newton's Law of Universal Gravitation with its formula.

Every two masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them: F = G·m₁m₂ / r².

What is the value of the universal gravitational constant G?

G = 6.67 × 10⁻¹¹ N·m²/kg².

How does gravitational force between two bodies change if the distance between them is doubled?

Since F ∝ 1/r², doubling the distance reduces the force to one-quarter (1/4) of its original value.

Derive the relation between g and G at Earth's surface.

Equating mg = GMm/R² gives g = GM/R², where M is Earth's mass and R is Earth's radius. Thus g depends on Earth's mass and radius, not on the falling object's mass.

Define centripetal force and give its direction and formula.

Centripetal force is the net inward force that keeps a body moving in a circular path, directed toward the centre. F = mv²/r = mω²r.

Define centripetal acceleration and give its formula.

Centripetal acceleration is the acceleration directed toward the centre of a circular path: a = v²/r = ω²r. It changes the direction of velocity, not its magnitude.

What is the relationship between linear velocity (v) and angular velocity (ω)?

v = rω, where r is the radius of the circular path and ω is the angular velocity in rad/s.

What provides the centripetal force for a car turning on a flat road and for a satellite orbiting Earth?

For the car: friction between tyres and road. For the satellite: the gravitational pull of the Earth.

Distinguish centripetal force from centrifugal force.

Centripetal force is the real inward force causing circular motion. Centrifugal force is an apparent (fictitious) outward force experienced in a rotating (non-inertial) reference frame.

Derive the orbital velocity of a satellite close to Earth's surface.

Setting gravitational force equal to centripetal force, GMm/r² = mv²/r, gives orbital velocity v = √(GM/r) = √(gr). Near the surface this is about 7.9 km/s.

What is the critical/minimum velocity needed to put a satellite into a low Earth orbit?

Approximately 7.9 km/s (about 8 km/s), the orbital velocity for an orbit just above Earth's surface.

What is escape velocity, give its formula, and its value for Earth.

Escape velocity is the minimum speed needed to escape a planet's gravity without further propulsion: v_e = √(2GM/R) = √(2gR). For Earth it is about 11.2 km/s.

What is a geostationary satellite and what is its orbital period and approximate height?

A geostationary satellite orbits in the equatorial plane with a period of 24 hours, so it appears fixed over one point on Earth. Its height is about 36,000 km above the surface.

Define stress and give its formula and SI unit.

Stress is the restoring force per unit cross-sectional area: stress = F/A. SI unit is the pascal (Pa) or N/m².

Define strain and state why it has no units.

Strain is the ratio of change in dimension to original dimension (e.g. ΔL/L). Being a ratio of like quantities, it is dimensionless and has no units.

State Hooke's Law and define Young's modulus.

Hooke's Law: within the elastic limit, stress is directly proportional to strain (stress ∝ strain). Young's modulus Y = stress/strain = (F·L)/(A·ΔL), a measure of a material's stiffness.

Define pressure and give its formula and SI unit.

Pressure is force acting normally per unit area: P = F/A. SI unit is the pascal (Pa), where 1 Pa = 1 N/m².

State the formula for pressure exerted by a column of liquid of depth h.

P = ρgh, where ρ is the liquid's density, g is gravitational acceleration, and h is the depth. Liquid pressure increases with depth and is independent of container shape.

State Pascal's Law.

Pressure applied to an enclosed (confined) fluid is transmitted equally and undiminished in all directions throughout the fluid (the principle behind hydraulic presses).

State Archimedes' Principle.

A body wholly or partly immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.

State the equation of continuity for fluid flow.

For an incompressible fluid, A₁v₁ = A₂v₂ (the volume flow rate Av is constant). Where the pipe is narrower, the fluid flows faster.

State Bernoulli's principle.

For a flowing incompressible non-viscous fluid, P + ½ρv² + ρgh = constant. Where fluid speed is higher, its pressure is lower (and vice versa).

Define an ideal fluid as assumed in Bernoulli's equation.

An ideal fluid is incompressible (constant density), non-viscous (no internal friction), and flows in a steady (streamline/laminar), irrotational manner.

State the difference between heat and temperature.

Heat is the total thermal energy transferred between bodies due to a temperature difference (measured in joules). Temperature is the measure of the average kinetic energy of a body's molecules (measured in kelvin/°C).

Name the three modes of heat transfer and briefly define each.

Conduction: heat transfer through a material by molecular collisions without bulk movement. Convection: heat transfer in fluids by the actual movement of heated particles. Radiation: heat transfer by electromagnetic waves, requiring no medium.

State the zeroth law of thermodynamics and the first law of thermodynamics.

Zeroth law: if two bodies are each in thermal equilibrium with a third, they are in equilibrium with each other (basis of temperature). First law: ΔQ = ΔU + W — heat added equals the increase in internal energy plus work done by the system (conservation of energy).

State the second law of thermodynamics (Kelvin and entropy statements).

Kelvin–Planck: no engine can convert all absorbed heat entirely into work in a cycle. Clausius/entropy: heat flows spontaneously from hot to cold, and the entropy of an isolated system never decreases.

State the combined (general) gas law, and Boyle's, Charles's, and Pressure (Gay-Lussac's) laws.

Combined: P₁V₁/T₁ = P₂V₂/T₂. Boyle's: at constant T, P ∝ 1/V. Charles's: at constant P, V ∝ T. Gay-Lussac's: at constant V, P ∝ T (T in kelvin).