⚙️ Physics — Mechanics
1. Physical Quantity
Mechanics is the branch of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects on their environment.
A physical quantity is a property of a body, substance, or phenomenon that can be quantified by measurement.
MEASUREMENT & ERRORS
- Absolute Error: Difference between true value and measured value.
- Relative Error: Ratio of absolute error to mean value.
- Percentage Error: Fractional error × 100.
2. Systems of Units
- CGS: Centimetre, Gram, Second
- FPS: Foot, Pound, Second
- MKS: Metre, Kilogram, Second
- SI: International System (adopted 1971)
FUNDAMENTAL QUANTITIES (SI)
| # | Quantity | Unit | Symbol |
|---|---|---|---|
| 1 | Length | Metre | m |
| 2 | Mass | Kilogram | kg |
| 3 | Time | Second | s |
| 4 | Electric current | Ampere | A |
| 5 | Temperature | Kelvin | K |
| 6 | Luminous intensity | Candela | cd |
| 7 | Amount of substance | Mole | mol |
Supplementary: Radian (plane angle) · Steradian (solid angle)
IMPORTANT DERIVED UNITS
| Quantity | SI Unit | Symbol |
|---|---|---|
| Force | newton | N |
| Energy / Work | joule | J |
| Speed | metre/second | ms⁻¹ |
| Frequency | hertz | Hz |
| Pressure | pascal | Pa |
| Power | watt | W |
| Surface tension | newton/metre | Nm⁻¹ |
| Viscosity | newton second/metre² | Nsm⁻² |
| Electric charge | coulomb | C |
| Electrical resistance | ohm | Ω |
| Impulse | newton second | Ns |
LENGTH · MASS · TIME
- 1 metre = distance travelled by light in vacuum in 1/299,792,458 of a second.
- 1 light year = 9.46 × 10¹⁵ m
- 1 parsec = 3.085 × 10¹⁵ m
- 1 angstrom (Å) = 10⁻¹⁰ m
- 1 nanometre (nm) = 10⁻⁹ m
- 1 Fermi = 10⁻¹⁵ m
- 1 kg = mass of 5.0188 × 10²⁵ atoms of carbon-12
- 1 amu = 1.66 × 10⁻²⁷ kg
- 1 second = 1/86400 of a mean solar day
SI PREFIXES
| Prefix | Symbol | Factor |
|---|---|---|
| exa | E | 10¹⁸ |
| peta | P | 10¹⁵ |
| tera | T | 10¹² |
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | μ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
| pico | p | 10⁻¹² |
| femto | f | 10⁻¹⁵ |
3. Scalar & Vector Quantities
- Scalar: Magnitude only (e.g., length, mass, time)
- Vector: Magnitude and direction (e.g., force, displacement, impulse)
DIMENSIONS
- Dimensions are the powers to which fundamental units are raised.
- Velocity: [L T⁻¹]
- Density: [M L⁻³]
4. Kinematics
Study of motion without considering its cause.
REST & MOTION
- Rest: No change in position with time
- Motion: Change in position with time
- Types: Rectilinear · Angular · Rotational
DISTANCE vs DISPLACEMENT
- Distance: Scalar, length of actual path (always ≥ 0)
- Displacement: Vector, change in position (can be +, −, or 0)
SPEED
- Formula: Speed = Distance / Time
- Average speed: Total distance / Total time
- For equal distances with speeds v₁, v₂: average = 2v₁v₂/(v₁ + v₂)
- For equal times with speeds v₁, v₂: average = (v₁ + v₂)/2
VELOCITY
- Formula: Velocity = Displacement / Time
- Relative velocity: |vAB| = √(vA² + vB² − 2vAvB·cos θ)
- Same direction (θ = 0°): vAB = vA − vB
- Opposite direction (θ = 180°): vAB = vA + vB
ACCELERATION
- Formula: Acceleration = Change in velocity / Time
- Positive: Velocity increases
- Negative (retardation): Velocity decreases
- SI unit: ms⁻²
EQUATIONS OF UNIFORMLY ACCELERATED MOTION
- v = u + at
- s = ut + ½at²
- v² = u² + 2as
- Free fall: replace 'a' with 'g'
- Vertical upward: replace 'a' with '−g'
- Distance in nth second: sn = u + (a/2)(2n − 1)
PROJECTILE MOTION
- Horizontal component (u cos θ) — constant
- Vertical component (u sin θ) — variable
- Time of flight: T = 2u sin θ / g
- Max height: H = u² sin²θ / (2g)
- Range: R = u² sin 2θ / g
- Rmax at θ = 45°
CIRCULAR MOTION
- Angular displacement (θ): arc / radius
- Angular velocity (ω): θ / t
- Linear velocity: v = ω · r
- Centripetal acceleration: v²/r = rω²
- Centripetal force: Fc = mv²/r = mrω²
5. Force & Newton's Laws
Force: Push/pull that can change the state of rest or motion. SI unit: Newton (N) · 1 N = 10⁵ dyne
FOUR FUNDAMENTAL FORCES
- Gravitational force
- Electromagnetic force
- Weak nuclear force
- Strong nuclear force (strongest)
NEWTON'S LAWS
- First Law (Inertia): Body remains at rest or uniform motion unless acted upon by external force.
- Second Law: F = Δp/Δt = ma (for constant mass)
- Third Law: Every action has an equal and opposite reaction.
MOMENTUM & IMPULSE
- Momentum: p = m·v (vector, kg ms⁻¹)
- Conservation of linear momentum: Rocket propulsion
- Impulse: Force × Time = Change in momentum
6. Friction
- Static friction: Opposes tendency to move (self-adjusting)
- Limiting friction: μsR = μsmg
- Kinetic friction: Opposes actual motion
- Sliding friction
- Rolling friction (smaller than sliding)
COEFFICIENT OF FRICTION
- Formula: μ = F / R
- Applications: Ball bearings, tyre threading, braking, walking
7. Work, Energy & Power
WORK
- Formula: W = F · s · cos θ
- Scalar, SI unit: Joule (J) · 1 J = 10⁷ erg
- Work = 0 when s = 0 or θ = 90°
ENERGY
- Kinetic Energy: K = ½mv² = p²/2m
- Potential Energy: U = mgh
- Forms: Solar · Fossil · Hydroelectric · Nuclear
- Einstein's Mass-Energy: E = Δmc²
POWER
- Formula: P = W/t = F·v
- SI unit: Watt (W)
- 1 HP = 746 W · 1 kW = 1000 W
8. Collision
- Elastic: Momentum & kinetic energy conserved
- Inelastic: Only momentum conserved
- Perfectly inelastic: Bodies stick together
9. Gravitation
NEWTON'S LAW OF GRAVITATION
- Formula: F = G·m₁·m₂ / r²
- G = 6.67 × 10⁻¹¹ Nm²kg⁻²
ACCELERATION DUE TO GRAVITY
- Formula: g = GM/R² ≈ 9.8 ms⁻²
- Maximum at poles, minimum at equator
- Decreases with height & depth
- Becomes zero at Earth's centre
ESCAPE VELOCITY
- Formula: ve = √(2GM/R) = √(2gR) ≈ 11.2 km/s
PLANETS (Distance from Sun)
Mercury → Venus → Earth → Mars → Jupiter → Saturn → Uranus → Neptune
KEPLER'S LAWS
- Elliptical orbits with Sun at one focus
- Areal speed is constant
- T² ∝ a³
SATELLITES
- Geostationary: height ≈ 36,000 km, T = 24 h
- Polar: height ≈ 800 km, T ≈ 84 min
- Formula: T = 2π√(R/g) ≈ 84.6 min (near Earth)
📌 Summary: Mechanics at a Glance
| Topic | Key Formula | Key Point |
|---|---|---|
| Speed | v = s/t | Scalar quantity |
| Velocity | v = d/t | Vector quantity |
| Acceleration | a = Δv/t | SI unit: ms⁻² |
| Force | F = ma | SI unit: Newton (N) |
| Work | W = F·s·cosθ | SI unit: Joule (J) |
| Kinetic Energy | K = ½mv² | Energy of motion |
| Potential Energy | U = mgh | Energy of position |
| Power | P = W/t | SI unit: Watt (W) |
| Gravitation | F = Gm₁m₂/r² | G = 6.67×10⁻¹¹ |
| Escape Velocity | ve = √(2gR) | ≈ 11.2 km/s |
KEY TAKEAWAYS FOR UPSC
- SI Fundamental Units: 7 — metre, kg, second, ampere, kelvin, candela, mole
- Scalar vs Vector: Scalar = magnitude only; Vector = magnitude + direction
- Equations of Motion: v = u + at, s = ut + ½at², v² = u² + 2as
- Projectile: Range maximum at 45°; Time of flight = 2u sinθ/g
- Newton's Laws: Inertia, F = ma, Action-Reaction
- Energy Conservation: Energy cannot be created or destroyed
- Escape Velocity: 11.2 km/s (Earth)
- Geostationary Satellite: 36,000 km, 24 hours
🎯 High-Yield Interactive UPSC Quiz (Physics — Mechanics)
Q1. What is the SI unit of force?
Correct Answer: B. The SI unit of force is Newton (N). 1 N = 1 kg·m/s².
Q2. Which of the following is a vector quantity?
Correct Answer: C. Displacement is a vector quantity (has both magnitude and direction). Mass, speed, and time are scalars.
Q3. The equation v = u + at represents:
Correct Answer: B. v = u + at is the first equation of motion (velocity-time relation).
Q4. At what angle is the range of a projectile maximum?
Correct Answer: C. The range of a projectile is maximum at an angle of 45°.
Q5. Which of Newton's laws explains the working of a rocket?
Correct Answer: C. Rocket propulsion works on Newton's third law — action and reaction are equal and opposite.
Q6. The value of acceleration due to gravity (g) is maximum at:
Correct Answer: B. The value of g is maximum at the poles and minimum at the equator.
Q7. What is the escape velocity from Earth's surface?
Correct Answer: B. Escape velocity from Earth's surface is approximately 11.2 km/s.
Q8. A geostationary satellite has a time period of:
Correct Answer: B. A geostationary satellite has a time period of 24 hours, matching Earth's rotation.
Q9. Which of the following is NOT a fundamental quantity in SI system?
Correct Answer: D. Force is a derived quantity, not a fundamental quantity in the SI system.
Q10. The centripetal force required for circular motion is provided by which force for electrons orbiting the nucleus?
Correct Answer: B. The electrostatic force of attraction between the electron and nucleus acts as the centripetal force.