OnlyGyaani • Class 11 Learning

Class 11 – Physics

Master 30 progressive topics covering measurement, mechanics, gravitation, properties of matter, thermodynamics, kinetic theory, oscillations and waves.

📏 Measurement and Motion

Physical World and Scope of Physics

Physics studies matter, energy, motion and the fundamental interactions of nature. It connects observations with mathematical laws and models, from microscopic particles to planets and galaxies.

Class 11 Physics builds the language needed for mechanics, heat and waves while showing how physical laws support engineering and modern technology.

Example: The same laws of motion explain a rolling ball, a moving car and the orbit of a satellite.

Practice: List five technologies that depend on principles of physics and identify the related branch.

Remember: Physics combines observation, experiment, measurement and mathematical reasoning.

Units, Dimensions and Dimensional Formulae

Physical quantities are expressed using numerical values and units. SI base units include metre, kilogram, second, ampere, kelvin, mole and candela; derived quantities are built from them.

Dimensions describe how a quantity depends on fundamental quantities. For example, velocity has dimension [LT⁻¹] and force has [MLT⁻²].

Example: Pressure = force/area, so its dimensional formula is [ML⁻¹T⁻²].

Practice: Find the dimensions of momentum, work and gravitational constant G.

Remember: Units may change between systems, but dimensions of a physical quantity do not.

Significant Figures and Measurement Errors

No experimental measurement is perfectly exact. Accuracy describes closeness to the true value, while precision describes repeatability. Errors may be systematic, random or related to instrument limitations.

Significant figures communicate the meaningful precision of a measured value and must be handled carefully during calculations.

Example: 0.00450 has three significant figures because leading zeros are not significant.

Practice: Calculate percentage error when a measured length is 19.8 cm and the accepted value is 20.0 cm.

Remember: A result should not claim more precision than the measurements used to obtain it.

Scalars, Vectors and Vector Resolution

Scalars have magnitude only, whereas vectors have both magnitude and direction. Vector addition follows geometric or component methods rather than ordinary arithmetic.

Resolving a vector into perpendicular components simplifies two-dimensional problems. For magnitude A at angle θ, components are A cosθ and A sinθ.

Example: A 10 N force at 60° has horizontal component 10 cos60° = 5 N.

Practice: Resolve a 20 m/s velocity at 30° above the horizontal into x and y components.

Remember: Direction is essential when adding or comparing vector quantities.

Motion in a Straight Line

One-dimensional kinematics describes position, displacement, speed, velocity and acceleration along a straight line. Average quantities describe an interval, while instantaneous quantities refer to a particular moment.

For constant acceleration, equations such as v=u+at and s=ut+½at² connect motion variables.

Example: Starting from rest with acceleration 2 m/s² for 5 s gives final velocity 10 m/s.

Practice: A car increases speed from 10 to 25 m/s in 5 s. Find its average acceleration.

Remember: Displacement can be zero even when distance travelled is not zero.

Position–Time and Velocity–Time Graphs

Motion graphs provide a visual description of kinematics. The slope of a position–time graph represents velocity, while the slope of a velocity–time graph represents acceleration.

The area under a velocity–time graph gives displacement over the chosen time interval.

Example: A horizontal line on a velocity–time graph means constant velocity and zero acceleration.

Practice: Sketch a velocity–time graph for an object accelerating uniformly from rest and explain its slope.

Remember: Always check what the axes represent before interpreting slope or area.

Motion in a Plane

Two-dimensional motion is analysed by treating horizontal and vertical components separately. Vector notation allows displacement, velocity and acceleration to be represented in a plane.

If the component motions are independent, each can be solved with suitable kinematic relations and then recombined.

Example: A boat crossing a river has one velocity relative to water and another due to the river current.

Practice: Add perpendicular velocity components 6 m/s east and 8 m/s north to find the resultant magnitude.

Remember: Perpendicular components combine using the Pythagorean theorem for magnitude.

Projectile Motion

A projectile moving under gravity has uniform horizontal velocity when air resistance is neglected, while its vertical velocity changes due to gravitational acceleration.

This produces a parabolic trajectory. Time of flight, maximum height and horizontal range depend on initial speed and launch angle.

Example: At the highest point of a projectile, vertical velocity is zero but horizontal velocity remains non-zero.

Practice: Explain why two projectiles launched with the same speed at complementary angles can have the same range on level ground.

Remember: Horizontal and vertical motions share the same time but obey different acceleration conditions.

🚗 Laws of Motion, Work and Rotation

Newton’s Laws of Motion

Newton’s first law introduces inertia, the second connects net force with rate of change of momentum, and the third states that interaction forces occur in equal and opposite pairs.

For constant mass, the second law becomes F=ma. Correct free-body diagrams are essential for applying these laws.

Example: A net force of 12 N on a 3 kg body produces acceleration 4 m/s².

Practice: Draw a free-body diagram for a book resting on a horizontal table.

Remember: Action and reaction forces act on different bodies, so they do not cancel each other on one body.

Friction and Its Applications

Friction opposes relative motion or the tendency of relative motion between contacting surfaces. Static friction adjusts up to a limiting value, while kinetic friction acts during sliding.

Friction is useful for walking, braking and gripping, but it can also cause energy loss and wear.

Example: Tyre-road friction allows a car to accelerate, turn and stop safely.

Practice: Explain why lubricants reduce friction in machines.

Remember: Static friction is not always equal to its maximum limiting value.

Uniform Circular Motion

In uniform circular motion, speed remains constant but velocity changes continuously because its direction changes. Therefore the body has centripetal acceleration directed toward the centre.

The required inward force is F=mv²/r and may be supplied by tension, gravity, friction or another interaction.

Example: Friction between tyres and road can provide centripetal force when a car turns on a level road.

Practice: Find centripetal acceleration for speed 10 m/s in a circle of radius 5 m.

Remember: Centripetal force is the name for the net inward force, not a separate new force.

Work and Kinetic Energy

Work is done when a force causes displacement. For a constant force, W=Fs cosθ. The work–energy theorem states that net work equals the change in kinetic energy.

Kinetic energy is K=½mv², showing that speed has a strong squared effect on a moving body’s energy.

Example: Doubling an object’s speed makes its kinetic energy four times as large if mass stays constant.

Practice: Calculate the kinetic energy of a 2 kg body moving at 6 m/s.

Remember: A force perpendicular to displacement does zero work.

Potential Energy, Conservation of Energy and Power

Potential energy is associated with position or configuration. Near Earth’s surface gravitational potential energy is mgh, while an ideal spring stores ½kx².

When only conservative forces act, mechanical energy remains constant. Power measures the rate of doing work: P=W/t.

Example: As a freely falling object loses gravitational potential energy, its kinetic energy increases.

Practice: Find the power needed to do 6000 J of work in 20 s.

Remember: Energy is measured in joules; power is measured in watts.

Centre of Mass and Linear Momentum

The centre of mass is the weighted average position of mass in a system. Translational motion of a system can often be described by following this point.

Total linear momentum is conserved when the net external force on a system is zero, making momentum powerful in collision and recoil problems.

Example: In an isolated collision, total momentum before collision equals total momentum after collision.

Practice: Find the centre of mass of two masses 2 kg and 3 kg placed 5 m apart along a line.

Remember: Internal forces can change individual momenta but not total momentum of an isolated system.

Rotational Motion and Moment of Inertia

Rotational motion uses angular displacement, angular velocity and angular acceleration as counterparts of linear variables. Moment of inertia measures resistance to angular acceleration and depends on mass distribution.

Rotational kinetic energy is ½Iω², where I is moment of inertia and ω is angular speed.

Example: Moving mass farther from the axis generally increases moment of inertia.

Practice: Compare qualitatively the rotation of two equal masses placed near and far from an axis.

Remember: Moment of inertia depends on both total mass and how that mass is distributed.

Torque and Angular Momentum

Torque describes the turning effect of a force and is given by τ=r×F, with magnitude rF sinθ. It plays a role in rotation similar to force in translation.

Angular momentum L is conserved when net external torque is zero. This explains many rotating-system behaviours.

Example: A door opens more easily when force is applied far from the hinge.

Practice: Explain why a skater spins faster when pulling the arms inward.

Remember: Greater perpendicular lever arm produces greater torque for the same force.

🌍 Gravitation and Properties of Matter

Universal Law of Gravitation

Every pair of masses attracts with force F=Gm₁m₂/r². The inverse-square dependence means gravitational force decreases rapidly as separation increases.

The law helps explain falling bodies, planetary motion and gravitational interactions across astronomical distances.

Example: Doubling the distance between two masses reduces their gravitational force to one quarter.

Practice: State how gravitational force changes if one mass triples while distance stays fixed.

Remember: Gravitational force is always attractive between ordinary masses.

Gravitational Potential, Escape Speed and Satellites

Gravitational potential describes potential energy per unit mass. Escape speed is the minimum speed required to move away without further propulsion under an ideal gravitational model.

Satellites remain in orbit because gravity supplies the centripetal acceleration required for their curved path.

Example: A satellite is continuously falling toward Earth but moves forward fast enough to keep missing the surface.

Practice: Explain why astronauts in orbit appear weightless even though Earth’s gravity is still acting.

Remember: Orbital weightlessness is associated with free fall, not absence of gravity.

Mechanical Properties of Solids

Solids deform when forces act on them. Stress measures internal force per area, strain measures relative deformation, and elastic moduli connect stress with strain within the elastic region.

Hooke’s law states that stress is proportional to strain for sufficiently small deformation in the linear elastic range.

Example: Young’s modulus compares tensile stress with longitudinal strain.

Practice: Distinguish elastic deformation from plastic deformation using an everyday material.

Remember: Elasticity concerns recovery of original shape, not simply softness or flexibility.

Pressure, Buoyancy and Fluid Flow

Fluid pressure acts in all directions and increases with depth in a stationary liquid. Pascal’s principle explains hydraulic systems, while Archimedes’ principle relates buoyant force to displaced fluid.

For ideal flow, continuity and Bernoulli’s principle connect fluid speed, pressure and height.

Example: Hydraulic brakes multiply force by transmitting pressure through an enclosed fluid.

Practice: Explain why an object can float when its average density is lower than that of the liquid.

Remember: Buoyant force equals the weight of displaced fluid.

Surface Tension, Viscosity and Capillarity

Surface tension arises from cohesive molecular forces at a liquid surface. Viscosity measures internal resistance to fluid flow, while capillary action results from surface tension combined with adhesive and cohesive forces.

These properties explain droplets, flow through tubes and liquid rise or fall in narrow capillaries.

Example: Water rises in a narrow glass tube because adhesive interaction with glass supports capillary rise.

Practice: Compare the flow of water and honey in terms of viscosity.

Remember: Higher viscosity means greater resistance to flow.

🌡️ Heat and Thermodynamics

Temperature, Thermal Expansion and Heat Transfer

Temperature indicates thermal state and determines the direction of spontaneous heat flow. Most materials expand when heated because average particle separation increases.

Heat can be transferred by conduction, convection and radiation, each important in different physical situations.

Example: Gaps are left in some structures to allow thermal expansion without damaging stress.

Practice: Identify the dominant heat-transfer method in a metal spoon, boiling water and sunlight reaching Earth.

Remember: Heat is energy in transfer; temperature is not the same thing as heat.

Specific Heat Capacity and Calorimetry

Specific heat capacity is the heat required to raise the temperature of unit mass by one degree. For a temperature change without phase change, Q=mcΔT.

Calorimetry applies conservation of energy: in an ideal isolated system, heat lost by hotter bodies equals heat gained by colder bodies.

Example: Water’s high specific heat helps it moderate temperature changes.

Practice: Calculate heat needed to raise 2 kg of water by 5°C using c=4200 J kg⁻¹ K⁻¹.

Remember: Temperature differences have the same numerical size in °C and K.

First Law of Thermodynamics

The first law expresses conservation of energy for thermodynamic systems. Heat supplied can change internal energy and/or be used to perform work.

Sign conventions must be stated consistently when using equations relating heat, internal energy and work.

Example: Heating a gas in a movable piston can both increase its internal energy and make it expand against external pressure.

Practice: Describe the energy transfers when a gas is compressed rapidly.

Remember: The first law is an energy-accounting principle, not a statement that temperature must remain constant.

Thermodynamic Processes and Heat Engines

Processes may be isothermal, adiabatic, isobaric or isochoric depending on which quantities remain constrained. Their pressure–volume behaviour differs.

A heat engine converts part of absorbed thermal energy into work while rejecting some heat to a colder reservoir; no real engine is perfectly efficient.

Example: In an isochoric process, volume is constant, so pressure may change as temperature changes.

Practice: Distinguish an isothermal process from an adiabatic process.

Remember: Engine efficiency is output work divided by heat absorbed from the hot reservoir.

Kinetic Theory of Gases

Kinetic theory models a gas as a huge number of particles in continuous random motion. Macroscopic pressure arises from molecular collisions with container walls.

Average molecular kinetic energy increases with absolute temperature, connecting microscopic motion with thermodynamic temperature.

Example: Heating a sealed rigid gas increases molecular speeds and therefore typically increases pressure.

Practice: Explain gas pressure using molecular collisions rather than treating pressure as a separate substance.

Remember: Absolute temperature is measured on the kelvin scale in kinetic-theory relations.

〰️ Oscillations and Waves

Simple Harmonic Motion

Simple harmonic motion occurs when restoring acceleration is directly proportional to displacement from equilibrium and directed toward equilibrium: a=−ω²x.

Displacement, velocity and acceleration vary periodically, while ideal mechanical energy alternates between kinetic and potential forms.

Example: An ideal mass–spring system performs SHM for small oscillations.

Practice: State where speed and acceleration are greatest during ideal SHM.

Remember: The negative sign in a=−ω²x shows acceleration points toward equilibrium.

Simple Pendulum and Time Period

For small angular displacements, a simple pendulum approximately performs SHM. Its time period is T=2π√(L/g), showing dependence on length and gravitational acceleration.

In the ideal small-angle model, period does not depend on the bob’s mass.

Example: Increasing pendulum length increases its time period.

Practice: Predict how the period changes if pendulum length becomes four times larger.

Remember: The standard pendulum formula assumes small oscillations and negligible resistance.

Wave Motion and Wave Equation

Waves transfer energy and information without transporting matter over the full propagation distance. Mechanical waves require a medium, while electromagnetic waves do not.

Wave speed, frequency and wavelength satisfy v=fλ. Frequency is set by the source, while speed depends on the medium.

Example: A 5 Hz wave with wavelength 2 m travels at 10 m/s.

Practice: Find wavelength when wave speed is 340 m/s and frequency is 170 Hz.

Remember: When a wave enters a new medium, frequency normally remains fixed while speed and wavelength may change.

Sound Waves, Standing Waves and Resonance

Sound is a mechanical wave produced by vibrations and requires a medium. Interference of waves can form standing-wave patterns with nodes and antinodes.

Resonance occurs when a system is driven near a natural frequency, producing large-amplitude oscillations when damping is limited.

Example: Air columns in musical instruments resonate at particular frequencies to produce notes.

Practice: Explain the difference between a node and an antinode in a standing wave.

Remember: Resonance depends on matching the driving frequency with a natural frequency of the system.