PAF Aeronautical Engineering Physics Syllabus

Physics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Physics in PAF Aeronautical Engineering, not a summary of it.

1. 1

   Measurement and Vectors

   3 topics

   • Physical Quantities and Units
   • Measurement and Errors
   • Vectors and Equilibrium
2. 2

   Mechanics

   5 topics

   • Kinematics
   • Dynamics and Newton's Laws
   • Work, Energy and Power
   • Circular Motion
   • Momentum and Collisions
3. 3

   Rotational and Fluid Dynamics

   4 topics

   • Rotational Equilibrium and Torque
   • Angular Momentum
   • Fluid Statics and Pressure
   • Fluid Dynamics and Bernoulli's Principle
4. 4

   Gravitation

   3 topics

   • Newton's Law of Gravitation
   • Orbital Motion and Satellites
   • Escape Velocity
5. 5

   Oscillations and Waves

   4 topics

   • Simple Harmonic Motion
   • Wave Motion and Properties
   • Sound and Acoustics
   • Doppler Effect
6. 6

   Thermodynamics

   4 topics

   • Heat and Temperature
   • Kinetic Theory of Gases
   • Laws of Thermodynamics
   • Heat Transfer
7. 7

   Optics

   2 topics

   • Geometrical Optics
   • Physical (Wave) Optics
8. 8

   Electricity and Magnetism

   5 topics

   • Electrostatics
   • Current Electricity and Circuits
   • Magnetism and Magnetic Fields
   • Electromagnetic Induction
   • Alternating Current
9. 9

   Modern Physics

   4 topics

   • Photoelectric Effect and Quantum Theory
   • Atomic Structure and Spectra
   • Nuclear Physics and Radioactivity
   • Electronics and Semiconductors

Physics flashcards for PAF Aeronautical Engineering

24 of 55 cards from the Physics deck — real questions with worked answers.

1. What is the difference between base quantities and derived quantities? Give two examples of each.

   Base quantities are fundamental and independent (e.g. length, mass, time). Derived quantities are formed by combining base quantities (e.g. velocity $= \frac{\text{length}}{\text{time}}$, force $= \text{mass}\times\text{acceleration}$).

2. List the seven SI base units with their physical quantities.

   Metre ($\text{m}$) for length, kilogram ($\text{kg}$) for mass, second ($\text{s}$) for time, ampere ($\text{A}$) for electric current, kelvin ($\text{K}$) for temperature, mole ($\text{mol}$) for amount of substance, and candela ($\text{cd}$) for luminous intensity.

3. What are the dimensions of force, energy, and pressure?

   Force: $[MLT^{-2}]$. Energy: $[ML^{2}T^{-2}]$. Pressure: $[ML^{-1}T^{-2}]$.

4. State the principle of homogeneity of dimensions and one use of dimensional analysis.

   An equation is dimensionally correct only if both sides have the same dimensions. Dimensional analysis is used to check the correctness of equations and to derive relationships between physical quantities.

5. Distinguish between precision and accuracy.

   Accuracy is how close a measurement is to the true value. Precision is how close repeated measurements are to one another (the fineness/consistency of measurement), independent of the true value.

6. What is the difference between random errors and systematic errors?

   Random errors vary unpredictably in size and sign and are reduced by averaging many readings. Systematic errors are consistent (same direction each time), arise from faulty instruments/zero errors, and are not reduced by averaging.

7. How do absolute, fractional, and percentage uncertainties relate?

   If absolute uncertainty is $\Delta x$ in a value $x$, then fractional uncertainty $= \frac{\Delta x}{x}$ and percentage uncertainty $= \frac{\Delta x}{x}\times 100\%$.

8. How do uncertainties combine when quantities are multiplied or divided, e.g. for $Q = \frac{A B}{C}$?

   Percentage (fractional) uncertainties add: $$\frac{\Delta Q}{Q} = \frac{\Delta A}{A} + \frac{\Delta B}{B} + \frac{\Delta C}{C}.$$

9. What is the least count of an instrument, and what are the least counts of a typical Vernier calliper and screw gauge?

   Least count is the smallest measurement an instrument can read. A typical Vernier calliper has a least count of $0.01\ \text{cm}$ ($0.1\ \text{mm}$); a screw gauge (micrometer) has $0.01\ \text{mm}$.

10. What is the difference between a scalar and a vector? Give one example of each.

    A scalar has magnitude only (e.g. mass, temperature, speed). A vector has both magnitude and direction (e.g. displacement, velocity, force).

11. For a vector $\vec{A}$ making angle $\theta$ with the x-axis, write its rectangular components and magnitude.

    Components: $A_x = A\cos\theta$, $A_y = A\sin\theta$. Magnitude: $A = \sqrt{A_x^{2} + A_y^{2}}$, with direction $\theta = \tan^{-1}\!\left(\frac{A_y}{A_x}\right)$.

12. Define the scalar (dot) product and the vector (cross) product of two vectors.

    Dot product: $\vec{A}\cdot\vec{B} = AB\cos\theta$ (a scalar). Cross product: $|\vec{A}\times\vec{B}| = AB\sin\theta$ (a vector perpendicular to both, direction given by the right-hand rule).

13. State the two conditions for complete equilibrium of a body.

    First condition (translational): $\sum \vec{F} = 0$, i.e. $\sum F_x = 0$ and $\sum F_y = 0$. Second condition (rotational): $\sum \vec{\tau} = 0$, the net torque about any point is zero.

14. What is the resultant magnitude of two vectors $\vec{A}$ and $\vec{B}$ with angle $\theta$ between them?

    $$R = \sqrt{A^{2} + B^{2} + 2AB\cos\theta}.$$

15. Distinguish between distance and displacement, and between speed and velocity.

    Distance is the total path length (scalar); displacement is the straight-line change in position with direction (vector). Speed is rate of distance (scalar); velocity is rate of displacement (vector).

16. Define average acceleration and instantaneous acceleration.

    Average acceleration $= \frac{\Delta v}{\Delta t}$, the change in velocity over a time interval. Instantaneous acceleration $= \lim_{\Delta t \to 0}\frac{\Delta v}{\Delta t} = \frac{dv}{dt}$, the acceleration at a single instant.

17. Write the three equations of motion for uniform acceleration.

    $$v = u + at,\quad s = ut + \tfrac{1}{2}at^{2},\quad v^{2} = u^{2} + 2as.$$

18. On a velocity-time graph, what do the slope and the area under the curve represent?

    The slope (gradient) gives the acceleration. The area under the velocity-time graph gives the displacement.

19. For a body in free fall (taking down as positive), what are its acceleration and the distance fallen from rest after time $t$?

    Acceleration $= g \approx 9.8\ \text{m s}^{-2}$ downward. Distance fallen from rest: $s = \tfrac{1}{2}g t^{2}$, and velocity $v = g t$.

20. For projectile motion, how are the horizontal and vertical motions treated, and what are the respective accelerations?

    They are treated independently. Horizontal motion has constant velocity (acceleration $= 0$); vertical motion has constant acceleration $g$ downward due to gravity.

21. Write the formulas for time of flight, maximum height, and range of a projectile launched at speed $v_0$ and angle $\theta$.

    $$T = \frac{2 v_0 \sin\theta}{g},\quad H = \frac{v_0^{2}\sin^{2}\theta}{2g},\quad R = \frac{v_0^{2}\sin 2\theta}{g}.$$

22. At what launch angle is the range of a projectile maximum (on level ground), and why?

    At $\theta = 45^{\circ}$, because $R = \frac{v_0^{2}\sin 2\theta}{g}$ is maximum when $\sin 2\theta = 1$, i.e. $2\theta = 90^{\circ}$.

23. What is the shape of a projectile's trajectory, and what are its velocity components at the highest point?

    The trajectory is a parabola. At the highest point the vertical velocity is zero and the horizontal velocity remains $v_0\cos\theta$.

24. State Newton's three laws of motion.

    First law (inertia): a body stays at rest or in uniform motion unless acted on by a net external force. Second law: $\vec{F} = m\vec{a}$. Third law: for every action there is an equal and opposite reaction.

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