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