Mechanics
The study of motion, forces, energy, and matter — the foundation of all physics.
A. Vectors & Scalars
Scalar vs Vector
| Type | Definition | Examples |
|---|---|---|
| Scalar | Has magnitude only | Mass, speed, time, temperature, energy, distance |
| Vector | Has magnitude and direction | Velocity, force, acceleration, displacement, momentum |
- Vector addition uses head-to-tail method or parallelogram law
- Resultant vector: single vector that produces the same effect as all combined vectors
Vector Components
Fₓ = F cosθ | F_y = F sinθ
Horizontal and vertical components of a vector F at angle θ
B. Kinematics (Motion)
Kinematics describes motion without considering its cause.
Terms & Definitions
| Term | Definition | Formula |
|---|---|---|
| Distance | Total path length (scalar) | — |
| Displacement | Shortest path start → end (vector) | s = final − initial position |
| Speed | Distance per unit time (scalar) | speed = d / t |
| Velocity | Displacement per unit time (vector) | v = s / t |
| Acceleration | Rate of change of velocity | a = (v − u) / t |
Equations of Motion
Uniformly accelerated motion
SUVAT Equations
v = u + at
s = ut + ½at²
v² = u² + 2as
s = (u + v)/2 × t
u = initial velocity · v = final velocity · a = acceleration · t = time · s = displacement
C. Dynamics — Newton's Laws
Newton's Three Laws
| Law | Statement | Formula / Example |
|---|---|---|
| 1st Law (Inertia) | A body stays at rest or in uniform motion unless acted on by external force | No net force → no acceleration |
| 2nd Law | Force equals mass × acceleration | F = ma |
| 3rd Law | Every action has an equal and opposite reaction | If A pushes B, B pushes A with equal force |
Newton's 2nd Law
F = ma
Weight W = mg | g = 9.8 m/s²
- Weight (W) = mg — force due to gravity on an object's mass
- Normal force: perpendicular contact force from a surface
- Friction force: opposes relative motion between surfaces
D. Forces, Torque & Momentum
Torque (Moment of Force)
Torque
τ = F × d
F = force (N) · d = perpendicular distance from pivot (m) · Unit: N·m
- Torque is the turning effect of a force about a pivot
- Principle of moments: Sum of clockwise moments = sum of anticlockwise moments (equilibrium)
Momentum & Impulse
Momentum
p = mv
Unit: kg·m/s
Impulse
J = Ft = Δp
Impulse = Force × time = change in momentum
- Conservation of Momentum: Total momentum before = after (no external forces)
- Elastic collision: both momentum and kinetic energy conserved
- Inelastic collision: only momentum conserved; KE is lost
E. Gravitation
Newton's Law of Universal Gravitation
Gravitational Force
F = G × m₁ × m₂ / r²
G = 6.67 × 10⁻¹¹ N·m²/kg² · r = distance between centres of mass
- g = 9.8 m/s² — acceleration due to gravity on Earth's surface
- Weight = mg
- Gravitational PE = mgh (near Earth's surface)
F. Energy — Kinetic & Potential
Types of Energy
| Type | Formula | Description |
|---|---|---|
| Kinetic Energy (KE) | KE = ½mv² | Energy due to motion |
| Gravitational PE | PE = mgh | Energy due to height above ground |
| Elastic PE | PE = ½kx² | Energy in a stretched/compressed spring |
| Work Done | W = F × d × cosθ | Energy transferred by a force over a distance |
| Power | P = W/t = Fv | Rate of doing work (Watts) |
- Conservation of Energy: energy cannot be created or destroyed, only converted
- At maximum height: KE = 0, PE = maximum
- At ground: KE = maximum, PE = 0
- Efficiency = (useful output / total input) × 100%
Key Energy Formulas
Kinetic Energy
KE = ½mv²
Potential Energy
PE = mgh
Work Done
W = F·d·cosθ
Power
P = W/t = Fv
⚡ MCQ Tip
F=ma (Newton 2nd). Momentum = mv. KE = ½mv². PE = mgh. g = 9.8 m/s².
Torque = F×d. Impulse = Ft = Δp. Conservation of momentum applies to all collisions.
Live Animation: Pendulum & Energy Conversion
Simple Pendulum — Energy Conversion
Watch kinetic ↔ potential energy exchange in real time
Quick MCQ Revision
| Formula | Meaning |
|---|---|
| F = ma | Newton's 2nd Law — Force = mass × acceleration |
| W = mg | Weight = mass × gravity (9.8 m/s²) |
| KE = ½mv² | Kinetic Energy |
| PE = mgh | Gravitational Potential Energy |
| p = mv | Momentum = mass × velocity |
| J = Ft = Δp | Impulse = Force × time = change in momentum |
| τ = F × d | Torque — turning effect of a force |
| F = Gm₁m₂/r² | Newton's Universal Gravitation |
| W = F·d·cosθ | Work Done |
| P = W/t = Fv | Power |
| v = u + at | SUVAT: velocity-time |
| s = ut + ½at² | SUVAT: displacement |
| v² = u² + 2as | SUVAT: velocity-displacement |
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