Physics Part I

Units and Measurement introduces the SI system of units—seven fundamental base quantities (length, mass, time, electric current, temperature, amount of substance, and luminous intensity) and their standard units—along with significant figures to express measurement precision and dimensional analysis to verify physical equations.

• 1SI system consists of seven base units (metre, kilogram, second, ampere, kelvin, mole, candela) for fundamental quantities; all other units are derived combinations of these.
• 2Significant figures represent measurement precision; rules govern addition/subtraction (match decimal places) and multiplication/division (match significant figure count of least precise value).
• 3Dimensions use square brackets [L], [M], [T], etc., to describe the nature of physical quantities independent of magnitude.
• 4Dimensional formulae express how base quantities combine to form a derived quantity; dimensional equations check if formulas are consistent.
• 5Dimensional analysis deduces relations among physical quantities and verifies equations, but cannot determine dimensionless constants like 2π in T = 2π√(l/g).

Motion in a Straight Line covers kinematics of one-dimensional motion, including velocity, acceleration, and kinematic equations for uniformly accelerated motion with real-world applications like free fall and stopping distance.

• 1Instantaneous velocity is the derivative dx/dt—the slope of the position-time curve at any instant
• 2Instantaneous acceleration is the derivative dv/dt—the slope of the velocity-time curve at any instant
• 3The area under a velocity-time curve represents displacement over that time interval
• 4Three kinematic equations for constant acceleration relate five quantities: v = v₀ + at, x = v₀t + ½at², and v² = v₀² + 2ax
• 5Free fall is uniform acceleration motion where a = –g = –9.8 m/s² (constant, regardless of initial velocity)

Class 11 Physics Chapter 3 covers motion in a plane using vector algebra, including projectile motion and uniform circular motion. Download the free NCERT PDF.

• 1Vectors have magnitude and direction; scalars have magnitude only. Vector addition follows triangle or parallelogram law, is commutative (A+B=B+A) and associative.
• 2Any vector can be resolved into components along perpendicular axes using unit vectors î and ĵ. Components relate to magnitude and direction angle by Ax = A cos θ, Ay = A sin θ.
• 3Motion in a plane is treated as two independent 1D motions. Using r = r₀ + v₀t + ½at² separately for x and y directions simplifies 2D kinematics.
• 4Projectile motion path is parabolic: y = (tan θ₀)x − gx²/(2v₀² cos² θ₀). Maximum height is hm = (v₀ sin θ₀)²/(2g), reached at time tm = v₀ sin θ₀/g.
• 5Horizontal range of projectile is R = v₀² sin 2θ₀/g, maximum when θ₀ = 45°. Time of flight is Tf = 2v₀ sin θ₀/g.

Laws of Motion comprises Newton's three fundamental laws that govern how forces affect the motion of bodies: the law of inertia, the relationship between force and acceleration, and the principle that forces always occur in equal and opposite pairs.

• 1Newton's First Law: A body at rest or in uniform motion remains so unless acted upon by net external force; this is inertia, not the absence of forces
• 2Newton's Second Law: F = dp/dt = ma expresses that force is proportional to rate of change of momentum and acts in the direction of acceleration
• 3Newton's Third Law: Forces always occur in pairs between two bodies; action and reaction are simultaneous and equal-opposite but act on different bodies
• 4Momentum p = mv is the product of mass and velocity; impulse equals force × time interval and equals change in momentum
• 5Static friction opposes impending motion (fs ≤ μsN); kinetic friction opposes actual relative motion (fk = μkN), with μk < μs

Work, energy, and power are fundamental physics quantities where work represents force applied over displacement, kinetic energy is the energy of motion, and power is the rate of work done—all related through the work-energy theorem which states that work done equals change in kinetic energy.

• 1Work is done by a force only when there is displacement in the direction of the force; W = (F cos θ)d = F·d
• 2Kinetic energy K = (1/2)mv² is always positive and represents energy due to motion
• 3Conservative forces (gravity, spring forces) depend only on initial and final positions; non-conservative forces (friction) depend on the path
• 4Mechanical energy is conserved for conservative forces: E = K + V(x) = constant, where V is potential energy
• 5Power is the time rate of doing work: P = dW/dt = F·v, measured in watts (1 W = 1 J/s)

The NCERT Class 11 Physics Chapter 6 PDF is free to download directly from the NCERT website. It covers systems of particles, rotational motion, centre of mass, torque, angular momentum, and moment of inertia.

• 1Centre of mass is defined by R = Σ(m_i r_i)/M; for symmetric bodies it coincides with the geometric centre.
• 2Linear velocity and angular velocity are related by v = ω × r, where ω is the angular velocity vector along the axis of rotation.
• 3Moment of inertia I = Σ(m_i r_i²) is the rotational analogue of mass; kinetic energy of rotation is K = (1/2)Iω².
• 4Torque τ = r × F and angular momentum L = r × p obey the rotational analogue of Newton's second law: τ = Iα and dL/dt = τ_ext.
• 5A rigid body in mechanical equilibrium must satisfy: (1) ΣF = 0 (translational) and (2) Στ = 0 (rotational).

Gravitation is the force of attraction between all material objects in the universe, inversely proportional to the square of the distance between them. Newton's law of universal gravitation governs both terrestrial and celestial phenomena, with the gravitational constant G = 6.67×10⁻¹¹ N m²/kg².

• 1All planets move in elliptical orbits with the Sun at one focus; the line joining a planet to the Sun sweeps equal areas in equal times; and the square of orbital period is proportional to the cube of semi-major axis (Kepler's laws)
• 2Gravitational force: F = Gm₁m₂/r² where G = 6.67×10⁻¹¹ N m²/kg²; independent of intervening matter and the nature of objects
• 3Acceleration due to gravity decreases with altitude: g(h) ≈ g(1 − 2h/Rₑ) for h << Rₑ and decreases with depth: g(d) = g(1 − d/Rₑ)
• 4Gravitational potential energy at distance r from Earth's center: W(r) = −GMₑm/r; total mechanical energy of orbiting satellites is negative
• 5Escape speed from Earth's surface: vₑ = √(2GMₑ/Rₑ) = √(2gRₑ) ≈ 11.2 km/s; independent of projectile mass or direction