Ch 03: Laws of Force & Motion

💥 Force — Introduction

External factor required for change in shape, direction and state of motion
Effect: Change in speed/direction/shape (Push, Pull, Hit)

Newton (N)

SI Unit

Dyne

CGS Unit

1 N = 10⁵ dyne

Conversion

📋 Types of Force

1. Contact Force

Requires physical contact
e.g. Frictional force, Muscular force

2. Non-Contact Force

No physical contact needed (Field force)
e.g. Gravitational force, Magnetic force

3. Balanced Force

Resultant force = Zero
a = 0; may remain at rest or move with constant velocity
Fnet = 200 − 200 = 0 N

4. Unbalanced Force

Resultant force ≠ Zero
a ≠ 0; velocity changes in magnitude or direction
Fnet = 400 − 200 = 200 N

⚠ Exam Trap

Balanced force → a = 0 (object stays at rest OR moves with constant velocity). Unbalanced → a ≠ 0. Gravitational force = Non-contact force (no touch required).

1️⃣ Newton's First Law — Law of Inertia

Also known as: Galileo's Law / Law of Inertia

An object at rest stays at rest; an object in motion stays in motion in a straight line
Until an external force acts on it
Gives the definition of Force and Inertia
e.g. Books on shelf, leaves falling, ball on inclined plane

Inertia

Proportional to mass
Types: Rest, Motion and Direction
Meaning: Opposes change, maintains stability
Leaves tend to remain at rest when a branch is suddenly shaken (inertia of rest)

Momentum

P = m × v
Unit: kg·m/s
Proportional to mass × velocity
Vector quantity

2️⃣ Newton's Second Law

Rate of change of momentum is proportional to applied force
F ∝ dp/dt → F = m(dv/dt)
F = ma
The expression of force is derived from 2nd law

F = ma

⚡ Impulse

Impulse = Average force × Time interval
I = F × Δt = ΔP
Unit: Ns
Practical examples: Hammer use, Players taking catch

I = F·Δt = m(v−u)

⚡ Worked Example

m=10g=0.01kg, u=0, v=10m/s
I = 0.01 × (10−0) = 0.1 Ns

3️⃣ Newton's Third Law — Action-Reaction Law

"Every action has an equal and opposite reaction"
F₁ = −F₂ (equal in magnitude, opposite in direction)
Action and reaction act on DIFFERENT bodies

Examples:Rocket launching, Rowing a boat, Swimming, Bouncing a ball, Firing a gun (recoil)

⚠ Exam Trap

1st Law = Inertia / Galileo's law. 2nd Law = F = ma (force defined here). 3rd Law = Action-Reaction. Action and reaction NEVER cancel each other (they act on different bodies).

🔄 Conservation of Linear Momentum

If external force = 0, total linear momentum remains conserved
F = dp/dt = 0 → P = constant
e.g. Rocket propulsion, Gun recoil, Boat moves back when person jumps

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

🎯 Collision — Worked Example

m₁ = 10 kg (moving right at 20 m/s)
m₂ = 4 kg (moving left at 20 m/s → u₂ = −20 m/s)
Combined mass = 14 kg (perfectly inelastic collision)

m₁u₁ + m₂u₂ = (m₁+m₂)v
10(20) + 4(−20) = 14v
200 − 80 = 14v
v = 120/14 = 8.57 m/s →

⚡ Quick Recall

Momentum = P = mv. Conservation only when external force = 0. Rocket works on conservation of momentum + Newton's 3rd law.

🧲 Friction — Introduction

Force acting along tangential direction between contact surfaces
Opposes relative motion
Parallel to contact surfaces
Dry friction: 0 ≤ f_s ≤ μ_sR; limiting static friction = μ_sR; sliding friction ≈ μ_kR

Causes of Friction

Irregularity of surfaces (rough surface → more friction)
Molecular bonds formed at contact points

Key Formula

f_lim = μ_sR; f_k ≈ μ_kR

μ = coefficient of friction
R = Normal reaction

📋 Types of Friction

Type	Explanation	Formula
Static Friction	Between surface & object BEFORE motion starts	—
Limiting Friction	Maximum value of static friction (just about to move)	Fs = μsR
Kinetic Friction	Between contact surfaces of MOVING objects	Fk = μkR
Rolling Friction	Weak friction when object ROLLS over surface (type of kinetic)	—
Sliding Friction	Friction due to SLIDING of object (type of kinetic)	—

Order:Static friction ≤ limiting friction; typically limiting > sliding > rolling resistance

⚠ Exam Trap

Rolling resistance is generally much smaller than sliding resistance under comparable conditions. Limiting friction is maximum static friction; actual static friction may be zero.

⚖️ Advantages vs Disadvantages of Friction

✅ Advantages

Walking and moving on ground
Brakes work due to friction
Writing on blackboard

❌ Disadvantages

Energy consumption (opposes motion)
Decrease in machine efficiency
Wear and tear of machine parts

🔧 Increasing vs Decreasing Friction

Increasing Friction

Making grooves in wheels (tyres)
Sprinkling sand on snow-covered roads
Making soles of shoes rough (hard rubber/leather)

Decreasing Friction

Polishing rough surfaces
Using lubricants between surfaces
Using materials with low coefficient of friction
Using ball bearings in machines
Streamlined motion in fluids

🌀 Centripetal vs Centrifugal Force

Centripetal Force

Acts towards the centre of circular path
Real force

F = mv²/r

Car turning on circular path
Electron around nucleus
Max speed on a level circular road at limiting friction: v_max = √(μsrg)
Ideal frictionless banking at design speed: tan θ = v²/rg

Centrifugal Force

Apparent force acting away from centre
Pseudo force (not real)

F = mv²/r

Cream extractor from milk
Washing machine dryer

⚠ Exam Trap

Centripetal = towards centre (real force). Centrifugal = away from centre (a pseudo or apparent force, not a real interaction force). The same magnitude formula applies, although the directions are opposite.

🔧 Torque / Moment of Force

Tendency of force to rotate an object around a fixed axis
Vector quantity
Unit: Newton-meter (Nm)

τ = r × F = rF sinθ

Couple

Two equal and opposite parallel forces with separated lines of action
Moment of couple = Force × Distance between parallel forces

Simple Machine

Equipment for lifting weights
An ideal lever works on the principle of moments; other simple machines use different geometries

🔩 Lever

Straight, bent, rigid rod
Principle: P × a = W × b
Mechanical Advantage (MA) = W/P = a/b

Effort (P):Force applied to lift load Fulcrum (F):Free rotation point Weight (W):Load to be lifted

Class	Position	MA	Effort Arm vs Load Arm	Examples
1st Class	Fulcrum between Load & Effort	>1, =1, or <1	Can be any	Scissors, See-saw, Hammer, Pliers, Beam balance
2nd Class	Load between Fulcrum & Effort	Always > 1	a > b	Wheelbarrow, nutcracker, bottle opener, hinged lemon squeezer
3rd Class	Effort between Fulcrum & Load	Always < 1	a < b	Tweezers, fishing rod, broom, human forearm lifting a load

⚠ Exam Trap

1st class lever = Fulcrum in middle (Scissors, See-saw). 2nd class = Load in middle (Wheelbarrow, Nutcracker). 3rd class = Effort in middle (Tweezers, Fishing rod). MA always >1 for 2nd class, always <1 for 3rd class.

⚡ Quick Recall — Order Trick

F = fulcrum, L = load, E = effort.
1st: L–F–E (fulcrum between load and effort)
2nd: F–L–E (load in middle)
3rd: F–E–L (effort in middle)

⚡ Chapter 03 — Laws of Force & Motion