IAT Physics Syllabus

Write the relation for limiting friction and define the coefficient of friction.

f_max = μ_s N, where N is the normal reaction and μ_s = coefficient of static friction = ratio of limiting friction to normal force.

What is the angle of repose?

The minimum angle of an inclined plane at which a body just begins to slide down; tan(angle of repose) = μ_s (coefficient of static friction).

What provides centripetal force and what is its formula?

Centripetal force points toward the centre of the circular path; F = mv²/r = mω²r, where ω is angular velocity.

In circular motion, distinguish centripetal and centrifugal force.

Centripetal force is the real inward force keeping a body on its circular path; centrifugal force is a pseudo (fictitious) outward force experienced only in a rotating (non-inertial) frame.

Give the minimum speed at the top of a vertical circle for a body to maintain contact.

v_top = √(gr), where g is acceleration due to gravity and r is the radius of the circle.

Define work done by a constant force and state when it is zero.

W = F·s·cosθ (force x displacement x cosine of angle between them); work is zero when the force is perpendicular to displacement (θ = 90°) or displacement is zero.

State the work-energy theorem.

The net work done on a body equals its change in kinetic energy: W_net = ΔKE = ½mv² - ½mu².

Write the formulas for kinetic energy and gravitational potential energy near Earth's surface.

Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh.

Distinguish between elastic and inelastic collisions.

In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision momentum is conserved but kinetic energy is not (some converts to heat/deformation).

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

Power is the rate of doing work, P = W/t; instantaneous power P = F·v (dot product of force and velocity). SI unit: watt (W).

Define the centre of mass of a system.

The point where the entire mass of a system may be considered concentrated; it moves as if all external forces act on the total mass placed there. For two masses: x_cm = (m₁x₁ + m₂x₂)/(m₁+m₂).

State the relation between torque and angular acceleration.

τ = Iα, where τ is torque, I is moment of inertia, and α is angular acceleration (the rotational analogue of F = ma).

State the law of conservation of angular momentum.

If no external torque acts on a system, its angular momentum L = Iω remains constant; reducing I increases ω (e.g., a spinning skater pulling in arms speeds up).

Define moment of inertia and state the factors it depends on.

Moment of inertia I = Σm_i r_i² measures rotational inertia; it depends on the total mass, its distribution relative to the axis, and the position/orientation of the rotation axis.

Give the moment of inertia of a solid sphere and a thin uniform rod (about its centre).

Solid sphere about a diameter: I = (2/5)MR²; thin rod about a perpendicular axis through its centre: I = (1/12)ML².

State the parallel axis theorem.

I = I_cm + Md², where I_cm is the moment of inertia about an axis through the centre of mass and d is the perpendicular distance to a parallel axis.

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

Every two masses attract 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, with G ≈ 6.67 x 10^-11 N·m²/kg².

How does acceleration due to gravity vary with height above Earth's surface?

g decreases with height: g_h = g (R/(R+h))² ≈ g(1 - 2h/R) for small heights, where R is Earth's radius.

Write the gravitational potential energy of two masses separated by distance r.

U = -G m₁m₂ / r; it is negative and approaches zero as r approaches infinity (taken as the reference).

Define escape velocity and give its formula from Earth's surface.

The minimum speed needed to escape a planet's gravity without further propulsion: v_e = √(2GM/R) = √(2gR) ≈ 11.2 km/s for Earth.

Give the orbital velocity of a satellite close to Earth's surface and its relation to escape velocity.

v_o = √(gR) ≈ 7.9 km/s; escape velocity v_e = √2 x v_o.

State Kepler's three laws of planetary motion.

1) Law of orbits: planets move in ellipses with the Sun at one focus. 2) Law of areas: the line joining a planet to the Sun sweeps equal areas in equal times. 3) Law of periods: T² ∝ a³ (square of period proportional to cube of semi-major axis).

What physical conservation principle does Kepler's second law (law of areas) represent?

Conservation of angular momentum, since the gravitational force is central (no torque about the Sun).

Define stress, strain, and Young's modulus.

Stress = force per unit area (F/A); strain = fractional change in dimension (ΔL/L); Young's modulus Y = longitudinal stress / longitudinal strain.

State Hooke's law and define the elastic limit.

Hooke's law: within the elastic limit, stress is directly proportional to strain (stress = modulus x strain). The elastic limit is the maximum stress up to which a body returns to its original shape after the load is removed.

State Pascal's law and the principle behind a hydraulic lift.

Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid. A hydraulic lift uses this so a small force on a small piston creates a large force on a large piston.

State Bernoulli's principle for fluid flow.

For a streamlined, non-viscous, incompressible flow, P + ½ρv² + ρgh = constant; where the fluid speed is higher, its pressure is lower.

State Archimedes' principle.

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

Distinguish heat from temperature.

Heat is energy transferred between bodies due to a temperature difference (a form of energy); temperature is a measure of the average kinetic energy of molecules and determines the direction of heat flow.

Name the three modes of heat transfer and the medium each requires.

Conduction (through solids, no bulk movement of matter), convection (in fluids via bulk movement), and radiation (electromagnetic waves, needs no medium).

State the zeroth law of thermodynamics and its significance.

If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other; it defines temperature as a measurable property.

State the first law of thermodynamics.

ΔQ = ΔU + ΔW: heat supplied to a system equals the increase in its internal energy plus the work done by the system. It is the law of conservation of energy.

For an isothermal and an adiabatic process, what stays constant?

Isothermal: temperature constant (ΔU = 0, so ΔQ = ΔW). Adiabatic: no heat exchange (ΔQ = 0, so ΔW = -ΔU), and PV^γ = constant.

State the second law of thermodynamics (Kelvin-Planck and Clausius statements).

Kelvin-Planck: no engine can convert heat entirely into work with no other effect. Clausius: heat cannot flow spontaneously from a colder to a hotter body without external work.

Give the efficiency of a Carnot engine.

η = 1 - T_c/T_h, where T_c and T_h are the cold and hot reservoir temperatures in kelvin; it is the maximum possible efficiency between two temperatures.

State the key assumptions of the kinetic theory of gases.

Gas molecules are point masses in constant random motion, with negligible volume and intermolecular forces, undergoing perfectly elastic collisions; time of collision is negligible compared to time between collisions.

What is the relation between the average kinetic energy of a gas molecule and temperature?

Average translational KE per molecule = (3/2)k_BT, where k_B is the Boltzmann constant; it depends only on absolute temperature, not on the gas type.

State the law of equipartition of energy.

In thermal equilibrium, each degree of freedom of a molecule has an average energy of (1/2)k_BT.

Define periodic and oscillatory motion, and give the relation between period and frequency.

Periodic motion repeats at regular intervals; oscillatory motion is periodic motion to-and-fro about a mean position. Frequency f = 1/T (T is the period); SI unit of frequency is hertz (Hz).

Define simple harmonic motion (SHM) and its defining force equation.

SHM is oscillatory motion where the restoring force is directly proportional to displacement and directed toward the mean position: F = -kx, giving acceleration a = -ω²x.

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

Simple pendulum: T = 2π√(L/g). Spring-mass: T = 2π√(m/k), where k is the spring constant.

How do kinetic and potential energy vary during SHM?

Total energy E = ½kA² is constant; KE is maximum at the mean position (zero displacement) and zero at extremes, while PE is maximum at the extremes and zero at the mean position.

Differentiate transverse and longitudinal waves with examples.

In transverse waves particles vibrate perpendicular to wave propagation (e.g., light, string waves); in longitudinal waves particles vibrate parallel to propagation, forming compressions and rarefactions (e.g., sound).

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

v = fλ (speed = frequency x wavelength).

Give the formula for the speed of a transverse wave on a stretched string.

v = √(T/μ), where T is the tension and μ is the linear mass density (mass per unit length) of the string.

On what factors does the speed of sound in air depend, and how does temperature affect it?

Speed of sound depends on the medium's properties; in a gas v = √(γP/ρ). It increases with temperature, approximately v ∝ √T (about +0.6 m/s per °C in air).

State the principle of superposition of waves.

When two or more waves overlap, the resultant displacement at any point equals the vector sum of the displacements due to individual waves.

What are beats and what is the beat frequency?

Beats are periodic variations in sound intensity from the superposition of two waves of slightly different frequencies; beat frequency = |f₁ - f₂|.

State the Doppler effect for sound.

The apparent change in frequency of sound due to relative motion between source and observer: frequency increases when they approach and decreases when they recede; f' = f (v ± v_o)/(v ∓ v_s).

What is resonance in oscillating systems?

Resonance occurs when the frequency of an external periodic force equals the natural frequency of a system, producing a large amplitude of oscillation.