BM 02: WORKSHOP CALCULATION & SCIENCE

1.Basic Arithmetic

1. Addition (+):
• Addition is the process of combining two or more numbers to find their total or sum.
2. Subtraction (-):
• Subtraction is the process of finding the difference between two numbers.
3. Multiplication (× or *):
• Multiplication is the process of repeated addition. It determines the total when a number is added to itself a certain number of times.
4. Division (÷ or /):
• Division is the process of sharing a quantity into equal parts. It determines how many times one number can be divided by another.

 

BODMAS Rules

1. B - Brackets:
• Perform calculations inside parentheses or brackets first.
2. O - Orders (Exponents and Roots):
• Evaluate expressions with exponents or roots.
3. D - Division:
• Perform division from left to right.
4. M - Multiplication:
• Perform multiplication from left to right.
5. A - Addition:
• Perform addition from left to right.
6. S - Subtraction:
• Perform subtraction from left to right.

2. Area, Volume

2.1. Area

Area is a measure of the amount of space inside a two-dimensional shape.

1. Rectangle:
• Area=length×width
2. Square:
• Area=side²
3. Triangle:
• Area= ×base×height
4. Circle:
• Area=π×radius²

 

2.2. Volume

Volume is a measure of the amount of space occupied by a three-dimensional object.

1. Cube

·       Volume=side³

2. Rectangular Prism:
• Volume=length × width × height
3. Cylinder:
• Volume=π × radius² × height
4. Sphere:
• Volume= ​π × radius³
5. Cone
• Volume= ​π × radius² × height
6. Pyramid:
• Volume= ​ × base area × height

3. Basic trigonometry and angles

3.1. Angles

1. Definition:
• An angle is formed by two rays that share a common endpoint, known as the vertex.
2. Types of Angles:
• Acute Angle: An angle less than 90°.
• Right Angle: An angle measuring exactly 90°.
• Obtuse Angle: An angle greater than 90° but less than 180°.
• Straight Angle: An angle measuring exactly 180°.
• Reflex Angle: An angle greater than 180° but less than 360°.
• A Full Circle is 360°. 

Basic Trigonometry

 Pythagorean Theorem

 

 

4.Units and Measurement

 

5.Conversion from metric to BS and vice versa

 Length 

 • 1 meter (m) ≈ 3.281 feet (ft) 

 • 1 foot (ft) = 0.3048 meters

 Mass 

 • 1 kilogram (kg) ≈ 2.205 pounds (lb) 

 • 1 pound (lb) ≈ 0.4536 kilograms 

 Volume 

 • 1 liter (L) ≈ 0.22 gallons (gal) 

 • 1 gallon (gal) ≈ 4.54609 liters

6. Basic idea of Work, Energy, Power & Pressure 

 1. Work 

 In physics, work is done when a force applied to an object causes it to move in the direction of the force. 

 work (W) = Force × Distance 

 2. Energy

 Energy is the ability to do work. There are various forms of energy, including kinetic energy (energy of motion), potential energy (energy stored due to position or state), thermal energy (heat energy), and more. 

 • Kinetic Energy (KE) = 1 2 mv2 where m is mass and v is velocity. 

 • Potential Energy (PE) = PE=mgh, where m is mass, g is the acceleration due to gravity, and h is height.

 3. Power 

 Power is the rate at which work is done or energy is transferred. 

 P=𝑊/ 𝑡 , where W is the work done, and t is the time taken. 

 4. Pressure 

 Pressure is defined as force per unit area.

 P=𝐹/ 𝐴 , where F is force, and A is the area over which the force is applied.

Basic Electricity

 What is Electricity?

Electricity is the movement of electric charge through a conductor.

Electricity is used to operate:

• Motors
• Fans
• Lights
• Computers
• Welding machines
• Pumps
• Industrial machines

An electrical circuit normally needs a complete path for current to flow.

Basic electrical circuit

Supply → Conductor → Load → Return path

Example:

Battery → Wire → Lamp → Wire → Battery

When the circuit is complete, current can flow and the lamp can operate.

Basic Electrical Principles

The main electrical quantities are:

1. Voltage
2. Current
3. Resistance
4. Power
5. Energy

These quantities are related to each other.

Basic relationship

Voltage causes current to flow.

Resistance opposes current flow.

Power is the rate of using electrical energy.

 Voltage

Voltage is the electrical potential difference between two points.

Voltage provides the electrical pressure that causes current to flow through a circuit.

Symbol

V

Unit

Volt (V)

Examples

• AA battery → approximately 1.5 V
• Car battery → approximately 12 V
• Domestic supply in Sri Lanka → approximately 230 V AC

Measuring voltage

A voltmeter is used to measure voltage.

A voltmeter is connected in parallel with the component or supply being measured.

 Resistance

Electrical resistance is the opposition to the flow of electric current.

Symbol

R

Unit

Ohm (Ω)

Electrical Power

Electrical power is the rate at which electrical energy is transferred or converted.

Symbol

P

Unit

Watt (W)

Formula

P = V × I

Example

Voltage = 230 V
Current = 2 A

P = 230 × 2

P = 460 W

Electrical Energy

Electrical energy is the amount of electrical work done or energy consumed by an electrical device.

Common units:

• Joule (J)
• Watt-hour (Wh)
• Kilowatt-hour (kWh)

Formula

Energy = Power × Time

Conductors

A conductor is a material that allows electric current to flow easily.

Common conductors

• Copper
• Aluminum
• Silver
• Gold
• Iron

Insulators

An insulator is a material that strongly resists the flow of electric current.

Examples

• Rubber
• Plastic
• Glass
• Ceramic
• Dry wood