Mechanical Reasoning - Cheat sheet
Your last-minute revision companion for mastering mechanical reasoning principles and solving exam problems quickly.
Gears and Wheels
Formulas
Speed Ratio = 1 / Size Ratio
Meaning
Speed of driven wheel = Speed of driver wheel ÷ Size ratio
Watch out
Remember it's INVERSE - smaller wheels turn FASTER, not slower
When to use
When calculating how fast one wheel turns relative to another
Turns = Driver turns × (Driver size ÷ Driven size)
Meaning
Number of complete turns made by driven wheel
Watch out
Always divide driver size by driven size, not the other way around
When to use
Finding exact number of rotations in gear problems
Important facts
- Large wheel drives small wheel → small wheel turns FASTER
- Small wheel drives large wheel → large wheel turns SLOWER
- Same size wheels turn at same speed
- In gear trains, multiply ratios to find final speed
- Direction alternates in directly connected gears
Key definitions
Driving Wheel
Example
Motor-connected wheel that turns other wheels
The wheel that provides power and initiates motion
Driven Wheel
Example
Wheel that rotates because another wheel turns it
The wheel that receives power from the driving wheel
Gear Ratio
Example
6cm gear driving 3cm gear has 2:1 ratio
Comparison of sizes between two connected gears
Diagrams to know
- Gear train diagrams showing multiple connected wheels
- Belt drive systems with pulleys of different sizes
- Wheel and axle mechanisms
Belt Drive Systems
Formulas
Fastest shaft = Smallest driving wheel + Largest driven wheel
Meaning
Best combination for maximum speed increase
Watch out
Don't confuse driving wheel with driven wheel - they have opposite effects
When to use
When asked which arrangement makes shaft turn fastest
Important facts
- Belts don't change direction of rotation (unlike direct gears)
- Belt can slip - less efficient than direct gear contact
- Smaller driving pulley = faster driven pulley
- Larger driving pulley = slower driven pulley
- Belt tension affects power transmission efficiency
Key definitions
Belt Drive
Example
Bicycle chain connecting pedal gear to wheel gear
System using flexible belt to transfer power between wheels
Pulley System
Example
Car engine driving alternator through belt
Wheels with grooved rims connected by belt or rope
Diagrams to know
- Pulley systems with belts
- Multiple pulley arrangements
- Belt drive speed calculations
Fluid Pressure and Flow
Formulas
Pressure = ρgh
Meaning
ρ = fluid density, g = gravity, h = depth/height
Watch out
Pressure increases with DEPTH, not height above surface
When to use
Calculating pressure at different depths in fluids
Common values
Value
101.3 kPa
Symbol
P₀
Quantity
Atmospheric pressure
Important facts
- Deeper locations have greater pressure
- Pressure acts equally in all directions at same depth
- Fluid flows from high pressure to low pressure
- Pressure depends on fluid density and depth only
- Same depth = same pressure regardless of container shape
Key definitions
Fluid Pressure
Example
Water pressure increases as divers go deeper
Force per unit area exerted by liquid or gas
Hydrostatic Pressure
Example
Pressure at bottom of swimming pool
Pressure in fluid at rest due to gravitational force
Diagrams to know
- U-tube manometer readings
- Pressure variation with depth diagrams
- Fluid flow direction indicators
Levers and Mechanical Advantage
Formulas
MA = Effort arm ÷ Load arm
Meaning
MA = mechanical advantage, measures force multiplication
Watch out
Longer effort arm = greater mechanical advantage, not shorter
When to use
Finding how much force is multiplied by lever
Effort × Effort arm = Load × Load arm
Meaning
Balance condition for levers in equilibrium
Watch out
Measure arms from fulcrum, not from ends of lever
When to use
When lever is balanced or finding unknown forces
Important facts
- First class: fulcrum between effort and load (seesaw)
- Second class: load between fulcrum and effort (wheelbarrow)
- Third class: effort between fulcrum and load (tweezers)
- Longer effort arm = less force needed
- Mechanical advantage > 1 means force is multiplied
Key definitions
Fulcrum
Example
Pivot point of seesaw or crowbar
Fixed point around which lever rotates
Effort Arm
Example
Distance from pivot to your hand on crowbar
Distance from fulcrum to where force is applied
Load Arm
Example
Distance from pivot to object being lifted
Distance from fulcrum to load being moved
Diagrams to know
- Three classes of levers with examples
- Force diagrams showing effort, load, and fulcrum
- Lever arm measurements
Must remember
- Inverse relationship: Small driving wheel = Fast driven wheel
- Speed ratio = 1 ÷ Size ratio (not size ratio directly)
- Pressure increases with depth in fluids
- In gear trains, multiply individual ratios for final result
- Belt drives don't reverse rotation direction
- Mechanical advantage = Effort arm ÷ Load arm
- Longer effort arm = less force needed to lift load
- Same depth in fluid = same pressure everywhere
- Count gear teeth or use diameter for size ratios
- Direction alternates in touching gears, stays same with belts
Last minute tips
- Draw arrows on gears to track rotation direction - saves time and prevents errors
- For speed calculations, always ask 'Is the driver bigger or smaller?' first
- In pressure problems, find the deepest point - it always has highest pressure
- Label fulcrum, effort, and load clearly in lever problems before calculating
- When multiple gears connect, work step-by-step through each connection
Comparison tables
Gear Size vs Speed Relationship
| Driving Gear | Driven Gear | Speed Change | Example | |
|---|---|---|---|---|
| Large to Small | Large | Small | Driven turns FASTER | 6cm → 3cm: 2× faster |
| Small to Large | Small | Large | Driven turns SLOWER | 3cm → 6cm: 2× slower |
| Same Size | Same | Same | Same speed | 3cm → 3cm: 1× speed |
Lever Classes Comparison
| Class | Arrangement | Example | Mechanical Advantage |
|---|---|---|---|
| First Class | Effort-Fulcrum-Load | Seesaw, Crowbar | Can be >1 or <1 |
| Second Class | Fulcrum-Load-Effort | Wheelbarrow, Nutcracker | Always >1 |
| Third Class | Load-Effort-Fulcrum | Tweezers, Fishing rod | Always <1 |
Diagrams
Mechanical Reasoning Concept Map
Overview of all mechanical reasoning topics and their relationships for quick review
Gear Speed Problem Solving Process
Step-by-step flowchart for solving gear speed problems systematically
Lever Classification System
Decision tree for classifying levers and determining their mechanical advantage properties