AP EAMCET / TS EAMCET Physics - Mechanics and Thermal Physics Syllabus

Where is the center of mass of a uniform rod, and how is the COM position calculated for discrete masses?

The COM of a uniform rod is at its geometric midpoint. For discrete masses: x_cm = (sum of m_i*x_i)/(sum of m_i).

Define torque (moment of force) and give its vector formula.

Torque is the turning effect of a force: tau = r x F, with magnitude tau = r F sin(theta). SI unit: newton-metre (N m).

What is the moment of inertia, and what is it for a solid sphere and a solid cylinder about their central axes?

Moment of inertia is rotational inertia: I = sum(m_i*r_i^2). Solid sphere about a diameter: I = (2/5)MR^2. Solid cylinder/disc about its axis: I = (1/2)MR^2.

State the theorem of parallel axes.

I = I_cm + Md^2, where I_cm is the moment of inertia about an axis through the center of mass and d is the perpendicular distance to a parallel axis.

Give the rotational analog of Newton's second law and the formula for rotational kinetic energy.

Torque tau = I*alpha (alpha = angular acceleration). Rotational KE = (1/2)I*omega^2.

State the law of conservation of angular momentum.

If the net external torque on a system is zero, its total angular momentum L = I*omega remains constant. Hence I1*omega1 = I2*omega2.

State Newton's law of universal gravitation.

Every two point masses attract each other with a force F = G*m1*m2/r^2, directed along the line joining them. G = 6.67 x 10^-11 N m^2/kg^2.

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

g_h = g(1 - 2h/R) for h << R, where R is Earth's radius. So g decreases with increasing height.

Give the formula for orbital velocity of a satellite and for escape velocity from Earth.

Orbital velocity v_o = sqrt(GM/r) = sqrt(g R^2/r). Escape velocity v_e = sqrt(2GM/R) = sqrt(2gR) ~ 11.2 km/s for Earth.

State Kepler's three laws of planetary motion.

1st (Law of Orbits): planets move in ellipses with the Sun at one focus. 2nd (Law of Areas): the line from Sun to planet sweeps equal areas in equal times. 3rd (Law of Periods): T^2 is proportional to a^3 (semi-major axis cubed).

Define gravitational potential energy of a two-body system and gravitational potential.

Gravitational PE U = -G*m1*m2/r (taken zero at infinity). Gravitational potential V = -GM/r (PE per unit mass).

Define stress and strain.

Stress = restoring force per unit area (F/A), unit N/m^2. Strain = ratio of change in dimension to original dimension (dimensionless), e.g., longitudinal strain = delta_L/L.

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

Hooke's law: within the elastic limit, stress is proportional to strain. Young's modulus Y = longitudinal stress/longitudinal strain = (F/A)/(delta_L/L).

Differentiate Young's modulus, bulk modulus, and modulus of rigidity.

Young's modulus (Y): tensile/compressive stress over linear strain. Bulk modulus (K): volume stress over volume strain (resistance to compression). Modulus of rigidity (eta): shear stress over shear strain.

What is Poisson's ratio?

Poisson's ratio = lateral strain / longitudinal strain. It is dimensionless, typically between 0 and 0.5 for most materials.

State Pascal's law and define pressure in a fluid.

Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished to all parts and the container walls. Pressure P = Force/Area; in a fluid at depth h, P = P0 + h*rho*g.

State Archimedes' principle.

A body wholly or partially immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced: F_buoyant = V*rho*g.

State the equation of continuity and Bernoulli's theorem for fluid flow.

Continuity: A1*v1 = A2*v2 (mass flow conserved). Bernoulli: P + (1/2)rho*v^2 + rho*g*h = constant along a streamline for an ideal fluid.

Define surface tension and capillary rise.

Surface tension = force per unit length acting along the surface (T = F/L), unit N/m. Capillary rise h = 2T cos(theta)/(r*rho*g), where theta is the contact angle and r is the tube radius.

State Newton's law of viscosity and give Stokes' law for a sphere falling in a fluid.

Viscous force F = -eta*A*(dv/dx), eta = coefficient of viscosity. Stokes' law: F = 6*pi*eta*r*v for a sphere of radius r moving with velocity v.

Define thermal expansion coefficients and give the relation between them.

Linear (alpha), areal (beta), and volume (gamma) expansion coefficients relate as beta = 2*alpha and gamma = 3*alpha (for isotropic solids).

Give the three modes of heat transfer with one distinguishing feature each.

Conduction: heat flow through a medium without bulk movement (solids). Convection: heat transfer by actual movement of fluid. Radiation: heat transfer by electromagnetic waves, requiring no medium.

State the first law of thermodynamics.

Heat supplied to a system equals the increase in internal energy plus work done by the system: dQ = dU + dW = dU + P*dV.

Distinguish isothermal, adiabatic, isobaric, and isochoric processes.

Isothermal: constant temperature (dU = 0). Adiabatic: no heat exchange (dQ = 0). Isobaric: constant pressure. Isochoric: constant volume (dW = 0).

State the second law of thermodynamics (Kelvin-Planck statement) and the efficiency of a Carnot engine.

Kelvin-Planck: no process can convert all absorbed heat completely into work. Carnot efficiency eta = 1 - T_cold/T_hot (temperatures in kelvin).

State the postulates and key result of the kinetic theory of gases for pressure.

Gas molecules are point-like, in constant random motion, with elastic collisions and negligible intermolecular forces. Pressure P = (1/3)(rho)(v_rms^2) = (1/3)(N/V)m(v_rms^2).

State the law of equipartition of energy and give the rms speed of gas molecules.

Each degree of freedom contributes (1/2)kT of energy per molecule. RMS speed v_rms = sqrt(3kT/m) = sqrt(3RT/M).

Differentiate heat and temperature.

Heat is energy transferred between bodies due to a temperature difference (unit: joule). Temperature is the measure of the average kinetic energy of molecules / degree of hotness (unit: kelvin).

Define simple harmonic motion and give the equations for its time period for a spring and a simple pendulum.

SHM: acceleration is proportional and opposite to displacement (a = -omega^2*x). Spring: T = 2*pi*sqrt(m/k). Simple pendulum: T = 2*pi*sqrt(L/g).

Give the speed of a transverse wave on a string and the equation for beat frequency.

Wave speed on a string v = sqrt(T/mu), where T is tension and mu is mass per unit length. Beat frequency = |f1 - f2| (difference of the two source frequencies).

State the Doppler effect formula for the observed frequency when source and observer move.

f' = f*(v +/- v_o)/(v -/+ v_s), where v is sound speed, v_o the observer speed, v_s the source speed; signs are chosen so that approach raises and recession lowers the frequency.