Air University Entry Test Physics Syllabus

What is the relationship between impulse and momentum?

Impulse equals the change in momentum: F.t = m vf - m vi = change in p. Impulse is a vector measured in N.s.

For a projectile launched at angle theta with speed v, write the formulas for time of flight, maximum height, and range.

Time of flight T = 2v sin(theta)/g; Maximum height H = v^2 sin^2(theta)/(2g); Range R = v^2 sin(2theta)/g. Range is maximum at theta = 45 degrees.

State the work-energy theorem.

The net work done on a body equals the change in its kinetic energy: W = (1/2)m vf^2 - (1/2)m vi^2 = change in KE.

Write the formulas for kinetic energy and gravitational potential energy.

Kinetic energy KE = (1/2)m v^2. Gravitational potential energy PE = mgh (near Earth's surface).

Define power and give its formula in terms of force and velocity.

Power is the rate of doing work: P = W/t. In terms of force, P = F.v (force times velocity). SI unit is the watt (W = J/s).

State the principle (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.

What is the difference between elastic and inelastic collisions regarding kinetic energy and momentum?

In both, momentum is conserved. In an elastic collision kinetic energy is also conserved; in an inelastic collision kinetic energy is not conserved (some is converted to heat/deformation).

Define centripetal acceleration and write its formula.

Centripetal acceleration is directed toward the centre of a circular path: a_c = v^2/r = r omega^2. SI unit m/s^2.

Write the formula for centripetal force and state its direction.

F_c = m v^2/r = m r omega^2, directed toward the centre of the circular path.

Relate linear velocity v to angular velocity omega, and define angular velocity.

v = r omega, where omega = (angular displacement)/(time) = theta/t, measured in rad/s. omega = 2pi f = 2pi/T.

Define moment of inertia and write rotational kinetic energy.

Moment of inertia I = sum(m r^2) measures rotational inertia about an axis. Rotational kinetic energy = (1/2)I omega^2.

Define angular momentum and state its conservation law.

Angular momentum L = I omega (= m v r for a point mass). It is conserved when the net external torque is zero; a smaller I gives a larger omega.

State Newton's law of universal gravitation with its formula.

Every mass attracts every other mass with a force F = G m1 m2 / r^2, directed along the line joining them, where G = 6.67 x 10^-11 N m^2/kg^2.

How does g relate to G, and how does g vary with altitude?

g = G M / R^2 at the surface. At height h, g' = G M/(R+h)^2, so g decreases with increasing altitude.

Derive/write the formula for the orbital velocity of a satellite near Earth's surface.

For a circular orbit, gravity provides centripetal force: v = sqrt(g R) = sqrt(G M / r). Near the surface v approx 7.9 km/s.

What is escape velocity and write its formula?

Escape velocity is the minimum speed to leave a planet's gravitational field: v_esc = sqrt(2 g R) = sqrt(2 G M / R). For Earth approx 11.2 km/s.

What conditions define a geostationary (geosynchronous) satellite and its orbital period?

It orbits in the equatorial plane in the same direction as Earth's rotation with a period of 24 hours (so it appears fixed above one point), at altitude approx 36,000 km.

Define simple harmonic motion (SHM) and state its defining condition.

SHM is oscillatory motion in which acceleration is directly proportional to displacement from the mean position and directed toward it: a = -omega^2 x.

Write the period of a simple pendulum and of a mass-spring system.

Simple pendulum: T = 2pi sqrt(L/g). Mass-spring: T = 2pi sqrt(m/k).

In SHM, where are velocity and acceleration maximum and minimum?

Velocity is maximum at the mean position and zero at the extremes. Acceleration is maximum at the extremes and zero at the mean position.

Write the expressions for total energy in SHM and how KE and PE vary.

Total energy E = (1/2)k A^2 = (1/2)m omega^2 A^2 (constant). KE is maximum at the mean position; PE is maximum at the extremes; they interchange so the sum stays constant.

Distinguish between transverse and longitudinal waves with examples.

In transverse waves particles vibrate perpendicular to wave direction (e.g. light, waves on a string). In longitudinal waves particles vibrate parallel to wave direction (e.g. sound waves).

Write the wave equation relating speed, frequency, and wavelength.

v = f lambda, where v is wave speed, f is frequency, and lambda is wavelength. Also f = 1/T.

What is the Doppler effect?

The Doppler effect is the apparent change in observed frequency/wavelength of a wave when there is relative motion between source and observer; frequency increases on approach and decreases on recession.

Define beats and give the formula for beat frequency.

Beats are periodic variations in loudness produced by superposition of two waves of slightly different frequencies. Beat frequency = |f1 - f2|.

State the conditions for constructive and destructive interference in terms of path difference.

Constructive interference: path difference = n lambda (n = 0,1,2,...). Destructive interference: path difference = (n + 1/2) lambda.

What does Young's double-slit experiment demonstrate, and write its fringe spacing formula.

It demonstrates the wave nature of light via interference. Fringe spacing y = lambda L / d, where d is slit separation and L is slit-to-screen distance.

What is polarization and what does it prove about the nature of light?

Polarization restricts light vibrations to a single plane. Only transverse waves can be polarized, so it proves that light is a transverse wave.

State the postulates (assumptions) of the kinetic theory of gases.

Gas consists of many tiny molecules in random motion; molecular volume is negligible vs container; collisions are perfectly elastic; no intermolecular forces except during collisions; average KE is proportional to absolute temperature.

State the first law of thermodynamics with its equation, and state the second law.

First law: Q = change in U + W (heat added equals change in internal energy plus work done by gas); it expresses energy conservation. Second law: heat flows spontaneously from hot to cold, and no engine can convert all heat into work (entropy of an isolated system never decreases).