Lesson 1: Applied Mechanics

Important SI Units

Mass = kilogram (kg)

Length = metre (m)

Area = metre^2 (m^2)

Volume = metre^3 (m^3)

Time = second (s)

Power = watt (W)

Force = Newton (N = kg-m/s^2)

Linear Velocity = metre/second (m/s)

Angular Velocity = radian/second (rad/s)

Linear acceleration = metre/second^2 (m/s^2)

Angular acceleration = radian/second^2 (rad/s^2)

Pressure = Pascal (Pa = N/m^2)

Density = kilogram/metre^3 (kg/m^3)

Work = Energy = joule (J = N-m)

Difference between SCALAR & VECTOR

Scalar: Have magnitude and unit

Vector: Have magnitude, direction and unit

Important Prefixes

Examples of Scalar Quantities:

Mass

Temperature

Time

Voltage

Work

Energy

Volume

Examples of Vector Quantities

Acceleration

Deceleration

Velocity

Force

Speed

Displacement

Weight

Momentum

Rotation Vector

tera (T) = 10^12 (LARGEST)

giga (G) = 10^9

mega (M) = 10^6

kilo (k) = 10^3

deci (d) = 10^-1

centi (c) = 10^-2

milli (m) = 10^-3

micro (μ) = 10^-6

nano (n) = 10^-9

pico (p) = 10^-12 (SMALLEST

New Conversions (that I took note of)

1 hour = 3600 seconds

1km^2 = 1000000m^2

1m^2 = 10000cm^2

Area & Volume Formulas

Area of sphere = 4 x pi x radius^2

Volume of a cube = length x breadth x height

Area of a circle = pi x radius^2

Circumference of circle = 2 x pi x radius

Vectors

4 quadrants of column vectors representation

1st quadrant = (x,y)

2nd quadrant = (-x, y)

3rd quadrant (-x, -y)

4th quadrant = (x, -y)

Trigonometry Formulas

TOH-CAH-SOH

Sine Rule: A/sin A = B/sin B

Cosine Rule: R^2 = P^2 + Q^2 - 2(P)(Q) cos B

Vector Formulas

Fx = x-component, Fy = y-component

Direction of Vector

tan ditto = Fy/Fx

click to edit

Only use when you do not know graphical representation!

Magnitude

F = square root of Fx^2 + Fy^2

Force components

Fx = F cos ditto

Fy = F sin ditto

Vector Diagrams

Triangle Rule

Parallelogram Rule

Vector Addition

Vector Subtraction

Types of Diagrams

Equal Vectors

Opposite Vectors

Multiplication of Vectors

Polygon Method

Graphical Representation

'Head to Tail' Drawing Method

Important Notes

If all vectors are added and can close, means resultant is zero

If cannot close, resultant is not zero