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| Physical Quantity | SI Unit | Symbol | |------------------|---------|--------| | Length | Metre | m | | Mass | Kilogram | kg | | Time | Second | s | | Temperature | Kelvin | K | | Electric Current | Ampere | A | | Amount of Substance | Mole | mol | | Luminous Intensity | Candela | cd |
RULES for counting significant figures:
1. All non-zero digits are significant: 325 → 3 sig figs
2. Zeros between non-zeros: 3005 → 4 sig figs
3. Leading zeros NOT significant: 0.005 → 1 sig fig
4. Trailing zeros with decimal: 3.50 → 3 sig figs
5. Trailing zeros without decimal: 300 → ambiguous (use 3×10²)
OPERATIONS:
Addition/Subtraction: Round to least decimal places
3.45 + 2.1 = 5.6 (not 5.55)
Multiplication/Division: Round to least sig figs
3.45 × 2.1 = 7.2 (not 7.245)
UNIFORM ACCELERATION (constant a):
v = u + at ... (1)
s = ut + ½at² ... (2)
v² = u² + 2as ... (3)
s_nth = u + a(2n−1)/2 ... (4) [distance in nth second]
Where: u = initial velocity, v = final velocity,
a = acceleration, t = time, s = displacement
FREE FALL (a = g = 9.8 m/s², u = 0):
v = gt
h = ½gt²
v² = 2gh
V-T GRAPH INTERPRETATIONS:
v(m/s)
│╲
│ ╲ Slope = (v−u)/t = a (deceleration)
│ ╲ Area = displacement (trapezoid)
│ ╲
└────────── t(s)
v(m/s)
│ /
│ / Slope = positive a (acceleration)
│ /
│ /
└────────── t(s)
v(m/s)
│─────────── Slope = 0 (uniform velocity, a=0)
│
└────────── t(s)
For V-T graph:
Slope of line = acceleration
Area under line = displacement (signed)
Projectile launched at angle θ with velocity u:
│ * (max height H)
│ * *
│ * *
│ * *
│ * *
│* *
└────────────────────────
│←───── Range R ────────→│
Components:
Horizontal: uₓ = u cosθ (constant, no acceleration)
Vertical: uᵧ = u sinθ (decreases due to gravity)
Equations:
x = u cosθ × t
y = u sinθ × t − ½gt²
At any time t:
vₓ = u cosθ (constant)
vᵧ = u sinθ − gt
Key formulas:
Time of flight: T = 2u sinθ/g
Maximum height: H = u² sin²θ / 2g
Range: R = u² sin2θ / g
Maximum Range when θ = 45°:
R_max = u²/g
Same range for θ and (90°−θ):
Example: θ=30° and θ=60° give same range
UNIFORM CIRCULAR MOTION:
v (tangential velocity)
↑
│
←────── ● ──────→ (centripetal force inward)
│ r
│
center
Speed constant, but velocity direction always changes
→ Acceleration exists! (centripetal acceleration)
Centripetal acceleration: a = v²/r = ω²r
Centripetal force: F = mv²/r = mω²r
ω = angular velocity (rad/s) = 2π/T = 2πf
T = time period, f = frequency
BLOCK ON SURFACE (no friction):
N (Normal force, upward)
↑
─────────────
│ Block │ ──→ F (Applied force)
─────────────
↓
mg (Weight, downward)
Equations: N = mg (vertical equilibrium)
F = ma (horizontal, Newton's 2nd)
BLOCK ON INCLINED PLANE:
N (perpendicular to surface)
↑ /
─────────────
│ Block │
─────────────/
↓ ╲
mg mg sinθ (along incline, causes motion)
Along incline: mg sinθ − f = ma
Perpendicular: N = mg cosθ
Types of Friction:
Static friction (fₛ): Prevents motion, can vary up to fₛ,max
Kinetic friction (fₖ): During motion, constant
fₛ,max = μₛN (μₛ = coefficient of static friction)
fₖ = μₖN (μₖ = coefficient of kinetic friction)
μₛ > μₖ always (static > kinetic)
Friction vs Applied Force graph:
f │ ─────── (fₛ,max = μₛN)
│ / ─ ─ ─ ─ ─ ─ (fₖ = μₖN)
│ /
│ / ← increasing f before motion
│────/
└──────────────────────── Applied Force
Work by constant force: W = F·d·cosθ
Work by variable force: W = Area under F-x graph
F(N)│
│ ╲
│ ╲ Area = Work done
│ ╲
│ ╲
└─────────── x(m)
Kinetic Energy: KE = ½mv²
Potential Energy (spring): PE = ½kx² (k = spring constant)
WORK-ENERGY THEOREM:
Net Work done = Change in Kinetic Energy
W_net = ΔKE = ½mv² − ½mu²
A (start, h above bottom)
╱│
╱ │h (height)
╱ │
╱ │
B─────────── bottom
At A: KE = 0, PE = mgh, ME = mgh
At B: KE = mgh, PE = 0, ME = mgh
KE at B = ½mv² = mgh
v = √(2gh)
Energy at A = Energy at B (conservation)
KEPLER'S 3 LAWS OF PLANETARY MOTION:
LAW 1 (Orbit shape):
Planets move in ELLIPSES with Sun at one focus
●─────────────────────────────●
/ \
/ ●Sun \
| |
\ /
\_________________________________/
LAW 2 (Equal areas):
Line from planet to Sun sweeps EQUAL AREAS in equal times
Near sun → faster (smaller arc, larger sweep area per unit time)
Far from sun → slower (larger arc, same area)
░░░ ░░░░░░░░░░░░░
░░░░░ ← same area → ░░░░░░░░░░░░░
░░░
LAW 3 (Period vs Distance):
T² ∝ r³ (T = period, r = semi-major axis)
T₁²/T₂² = r₁³/r₂³
ESCAPE VELOCITY: Minimum velocity to escape gravitational field
vₑ = √(2gR) = √(2GM/R)
For Earth:
R = 6.4 × 10⁶ m, g = 9.8 m/s²
vₑ = √(2 × 9.8 × 6.4×10⁶) = 11.2 km/s = 11,200 m/s
For Moon:
gₘₒₒₙ = g/6, Rₘₒₒₙ = R/3.67
vₑ,moon ≈ 2.4 km/s (much smaller)
That's why moon has no atmosphere!
P-V DIAGRAM (Pressure vs Volume):
P │
│ Isothermal (T=const): PV = const (hyperbola)
│ ╲
│ ╲
│ ╲
└──────── V
P │ Adiabatic (Q=0): steeper than isothermal
│ │╲
│ │ ╲
│ │ ╲
└────────── V
P │ Isobaric (P=const): horizontal line
│───────────
│
└──────── V
P │ Isochoric (V=const): vertical line
│ │
│ │
│ │
└──────── V
Area under PV curve = WORK DONE by gas
ZEROTH LAW:
If A is in thermal equilibrium with B, and B with C,
then A is in equilibrium with C
→ Defines TEMPERATURE
FIRST LAW (Energy conservation):
ΔU = Q − W
Q = heat added, W = work done by system
Process Q W ΔU
Isothermal ≠0 ≠0 =0
Adiabatic =0 ≠0 ≠0
Isochoric ≠0 =0 ≠0
Isobaric ≠0 ≠0 ≠0
SECOND LAW:
Heat flows spontaneously from HOT to COLD only
Efficiency of heat engine < 100%
η = 1 − T_cold/T_hot (Carnot efficiency, max possible)
THIRD LAW:
At absolute zero (0 K), entropy = 0
It is impossible to reach absolute zero (only approach it)
SHM POSITION DIAGRAM:
x │ A (amplitude)
│ ╭───╮
│ ╭ ╮
│ ╭ ╮
─────┼──────────────────── t
│ ╰ ╯
│ ╰ ╯
│ −A ╰╯
x = A sin(ωt + φ) [position]
v = Aω cos(ωt + φ) [velocity] → max at center, 0 at ends
a = −Aω² sin(ωt) [acceleration] → max at ends, 0 at center
For simple pendulum:
T = 2π√(L/g) [T = period, L = length]
f = 1/T = (1/2π)√(g/L)
For spring-mass:
T = 2π√(m/k) [k = spring constant]
Progressive wave equation:
y = A sin(ωt − kx) [traveling in +x direction]
A = amplitude, ω = angular frequency, k = wave number
k = 2π/λ (λ = wavelength)
v = ω/k = fλ
Types of waves:
Transverse: displacement ⊥ direction of travel (light, string)
Longitudinal: displacement ∥ direction of travel (sound)
Sound speed in medium:
In solid: v = √(Y/ρ) [Y = Young's modulus]
In liquid: v = √(B/ρ) [B = Bulk modulus]
In gas: v = √(γP/ρ) [γ = adiabatic index ≈ 1.4 for air]
Class 11 Physics complete NCERT notes — units, kinematics, laws of motion, work-energy, gravitation, properties of matter, thermodynamics, waves and oscillations with diagrams and solved problems.
64 pages · 2.4 MB · Updated 2026-03-11
Scalar: Has only magnitude. Examples: mass, speed, temperature, time, distance, energy. Vector: Has both magnitude and direction. Examples: velocity, force, acceleration, displacement, momentum. Vectors follow vector addition (parallelogram law), not simple algebraic addition.
v = u + at; s = ut + ½at²; v² = u² + 2as. These apply when acceleration is uniform (constant). u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement.
ΔU = Q − W. Change in internal energy of a system = Heat added to system minus Work done by system. It is the law of conservation of energy applied to thermodynamic systems. For isothermal process: ΔU = 0, so Q = W. For adiabatic: Q = 0, so ΔU = −W.
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