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Applied Mechanics - Coggle Diagram
Applied Mechanics
Prefixes for Units of Measurement (b)
Giga- (G): 10^9 (billion)
Milli- (m): 10^(-3) (thousandth)
Mega- (M): 10^6 (million)
Micro- (μ): 10^(-6) (millionth)
Kilo- (k): 10^3 (thousand)
Nano- (n): 10^(-9) (billionth)
How are Vectors different from Scalars (c)
Scalars
Quantities that have only magnitude (e.g., mass, temperature).
Vectors
Quantities that have both magnitude and direction (e.g., velocity, force).
Adding up Vectors (e)
Using the parallelogram law or the triangle law.
To add two vectors, you can place them head to tail and then draw a vector from the tail of the first vector to the head of the second vector.
The resultant vector is the vector from the tail of the first vector to the head of the second vector.
Representation of Vectors (d)
Component Form
Vectors are represented as a sum of their horizontal and vertical components.
Arrow Notation
A vector is represented by an arrow where the length represents magnitude and the direction of the arrow indicates the direction.
Trigonometry and Pythagoras Theorem in Right-Angled Triangles (f)
Pythagoras Theorem: In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Trigonometric Ratios: In a right-angled triangle, sine, cosine, and tangent of an angle are defined as the ratios of the lengths of the sides.
Sine Law and Cosine Law (g)
Sine Law: For any triangle ABC, the ratio of the length of a side to the sine of its opposite angle is the same for all three sides
Cosine Law: Cosine Law: For any triangle ABC, the square of the length of a side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of these lengths and the cosine of their included angle
Unit of measurement (a)
Second (s): Measures time. It is a basic unit.
Ampere (A): Measures electric current. It is a basic unit.
Kilogram (kg): Measures mass. It is a basic unit.
Newton (N): Measures force. It is a derived unit.
Meter (m): Measures length. It is a basic unit.
oule (J): Measures energy. It is a derived unit.
