Std. 11
Physics

Physics studies matter, energy, motion, interactions and the laws that describe them. A scientific model connects observation, measurement, mathematics and experiment.

Physical quantities are expressed using units. Dimensional analysis checks whether an equation is dimensionally consistent and helps identify the dimensions of derived quantities.

Significant figures indicate the precision of a measured quantity. Calculations should not claim greater precision than the data support.

Measurements contain uncertainty. Absolute error, relative error and percentage error help describe the reliability of a measured value.

A scalar has magnitude only; a vector has magnitude and direction. Vector addition follows geometric or component methods.

A vector A can be resolved into perpendicular components such as Aₓ=A cosθ and Aᵧ=A sinθ. Components allow complicated vector problems to be handled algebraically.

The slope of a graph often represents a physical quantity. Always label axes with units, choose an appropriate scale and interpret the graph physically.

Distance is the total path length and is a scalar. Displacement is the directed change in position and is a vector.

Average speed is total distance divided by total time. Average velocity is displacement divided by time. Instantaneous velocity describes motion at a particular instant.

Acceleration is rate of change of velocity: a=Δv/Δt. It can result from a change in speed, direction or both.

For constant acceleration: v=u+at, s=ut+½at², v²=u²+2as. These equations apply only when acceleration is constant.

The slope of a displacement-time graph gives velocity. The slope of a velocity-time graph gives acceleration; the area under a velocity-time graph gives displacement.

A projectile has independent horizontal and vertical motions. Neglecting air resistance, horizontal velocity remains constant while vertical motion has acceleration g.

Velocity of A relative to B is v_AB=v_A−v_B. This is useful when describing one moving object from the frame of another.

A body remains at rest or in uniform straight-line motion unless acted upon by a net external force. It expresses inertia.

The net force equals rate of change of momentum. For constant mass, F=ma. Force is a vector, so direction matters.

For every action there is an equal and opposite reaction. The two forces act on different bodies, so they do not cancel each other on one free-body diagram.

Momentum is mass times velocity: p=mv. For an isolated system, total momentum remains constant.

Impulse is force multiplied by time interval and equals change in momentum: J=FΔt=Δp. It explains why increasing collision time can reduce average force.

Friction opposes relative motion or the tendency of relative motion. Static friction adjusts up to a limiting value; kinetic friction acts when surfaces slide.

For uniform circular motion, centripetal acceleration is a_c=v²/r=ω²r and the required inward force is F_c=mv²/r. Centripetal force is not a new type of force; it is the net inward force.

A body is in translational equilibrium when the vector sum of external forces is zero. For a body in equilibrium under several forces, use a clear free-body diagram before resolving components.

Work is done when a force produces displacement. For a constant force, W=Fs cosθ. Work is a scalar quantity.

Kinetic energy is energy due to motion: K=½mv². It increases with the square of speed.

The net work done on a particle equals its change in kinetic energy: W_net=ΔK.

Near Earth's surface, gravitational potential energy is U=mgh. The zero level can be chosen conveniently, but energy differences must be consistent.

Power measures the rate of doing work: P=W/t. Instantaneous power can be written P=F·v.

When only conservative forces do work, kinetic plus potential energy remains constant. Non-conservative forces such as friction convert mechanical energy into other forms.

In an isolated system, momentum is conserved in collisions. Kinetic energy is conserved only in elastic collisions; in inelastic collisions some becomes other forms of energy.

The centre of mass represents the mass-weighted average position of a system. For particles, R_cm=Σmᵢrᵢ/Σmᵢ.

Torque measures the turning effect of a force: τ=r×F. Its magnitude is τ=rF sinθ.

Angular velocity is rate of angular displacement: ω=dθ/dt. For circular motion, v=rω.

α=dω/dt. For constant angular acceleration, rotational equations mirror the linear equations with θ, ω and α replacing s, v and a.

Moment of inertia measures resistance to rotational acceleration and depends on how mass is distributed relative to the axis.

For a rigid body about a fixed axis, L=Iω. If external torque is negligible, angular momentum is conserved.

K_rot=½Iω². Rolling bodies can possess both translational and rotational kinetic energy.

For complete mechanical equilibrium, both resultant force and resultant torque must be zero. Choose a convenient point for taking moments.

Every two masses attract each other with force F=Gm₁m₂/r², directed along the line joining their centres.

Near a spherical Earth, g=GM/R². The value changes with altitude, depth and latitude.

Gravitational potential at distance r from a mass M is V=−GM/r; gravitational potential energy of mass m is U=−GMm/r.

Escape velocity is the minimum speed required to escape a body's gravitational field without further propulsion: v_e=√(2GM/R)=√(2gR) for a spherical body.

For circular orbital motion, gravitational force provides centripetal force. Orbital speed is v=√(GM/r) and the orbital period follows from the same balance.

A geostationary satellite has an orbital period equal to Earth's rotation period, moves in the equatorial plane and appears fixed over one longitude under ideal conditions.

Apparent weightlessness occurs when a person and supporting surface are in free fall together, so the normal reaction becomes very small or zero.

Elasticity is the ability of a material to regain its original shape after deforming forces are removed, within its elastic limit.

Stress is force per unit area: stress=F/A. Strain is fractional deformation: strain=ΔL/L.

Young's modulus is the ratio of longitudinal stress to longitudinal strain: Y=(F/A)/(ΔL/L).

Pressure is normal force per unit area: P=F/A. Fluid pressure increases with depth: P=P₀+ρgh.

Pressure applied to an enclosed fluid is transmitted undiminished in all directions. Hydraulic machines use this principle to multiply force.

A body immersed in a fluid experiences an upward buoyant force equal to the weight of fluid displaced. This explains floating and apparent loss of weight.

Surface tension arises from cohesive forces at a liquid surface and tends to minimise surface area. It explains droplets, capillary effects and insects supported on water.

Viscosity describes internal resistance to fluid flow. For laminar flow through a narrow tube, Poiseuille's law gives Q∝ΔP r⁴/(ηl).

For steady ideal fluid flow along a streamline, P+½ρv²+ρgh=constant. Higher flow speed is associated with lower static pressure under the stated assumptions.

Temperature indicates thermal state; heat is energy transferred because of a temperature difference. Heat is not a substance stored inside a body.

Heating generally increases average molecular separation. Linear expansion can be described by {f('ΔL=αL₀ΔT')}.

Heat transfer for a substance can be calculated using Q=mcΔT. In an ideal calorimeter, heat lost equals heat gained.

Energy conservation for a thermodynamic system is expressed as ΔQ=ΔU+ΔW when ΔW is work done by the system.

In an isothermal process temperature remains constant. In an adiabatic process no heat enters or leaves the system: Q=0.

The second law introduces direction to natural processes and the concept of entropy. Heat does not spontaneously flow from a colder body to a hotter body without external work.

A heat engine converts part of absorbed heat into work. Efficiency is η=W/Q_H=1−Q_C/Q_H. No heat engine can convert all supplied heat into work in a cyclic process.

A refrigerator transfers heat from a colder region to a warmer region using external work. Its performance is described by coefficient of performance rather than ordinary efficiency.

Boyle's law: PV=constant at constant temperature. Charles' law: V/T=constant at constant pressure. Avogadro's law relates volume to amount at fixed temperature and pressure.

PV=nRT connects pressure, volume, temperature and amount of gas. Temperature must be measured in kelvin.

A gas consists of rapidly moving particles. In the ideal model, intermolecular forces are neglected except during collisions, and collisions are elastic.

Gas pressure results from molecular collisions with container walls. The kinetic-theory relation is PV=⅓Nm⟨c²⟩.

Absolute temperature measures average translational kinetic energy. For an ideal gas, average K per molecule=3kT/2.

Degrees of freedom count independent ways in which a molecule can store energy. Equipartition connects each quadratic degree of freedom with average energy proportional to kT.

Characteristic speeds include rms speed: c_rms=√(3RT/M). Higher temperature increases molecular speeds, while greater molar mass lowers them at the same temperature.

Periodic motion repeats after a fixed time interval. Simple harmonic motion is a special periodic motion in which restoring acceleration is proportional to displacement and directed toward the mean position.

For SHM, a=−ω²x. Displacement may be written x=A sin(ωt+φ).

Frequency and period are related by f=1/T. Angular frequency is ω=2πf.

Total mechanical energy of ideal SHM is constant: E=½kA²=½mω²A². Energy alternates between kinetic and potential forms.

For small oscillations, the time period is T=2π√(l/g). The small-angle condition is important for this formula.

A wave transfers energy and information without transporting matter bodily from one place to another. Mechanical waves require a medium; electromagnetic waves do not.

v=fλ. Frequency is determined by the source, while wave speed depends mainly on the medium and conditions.

When waves overlap, their displacements add according to superposition. Interference can produce nodes and antinodes in stationary waves.

Sound in air is a longitudinal mechanical wave. Pitch depends mainly on frequency, while loudness is related to amplitude and intensity.