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Component Form of Vectors
it simplifies operations by breaking down vectors into their individual components
Unit Vector
It has a magnitude of 1 and no units as it only aims to point to a direction in space.
It has a caret (^) to distinguish it from ordinary vectors.
common for three dimensions as it requires z-axis
Unit Vector Formula (does not include caret)
A = Axi + Ayj + Azk
Dot Product
Known as the scalar product, it is equal to A • B. The quantity will end up being scalar.
Definition of Dot Product
|A|•|B|cos(angle between both vectors)
Angles and Dot Product
If the angle is zero, then the formula is |A|•|B|
If the angle is 90º, then the dot product is zero.
Otherwise, assume the formula as normal
Vector Product
measures how parallel the vectors are
also known as the cross product
the product is a vector
C = ABsinΘ
Work
measure of energy transfer that occurs when an object is moved over a distance by an external force
Positive Work
force and displacement have components that move in the same direction
Negative Work
force and displacement have components that move in the opposite direction
Zero Work
Occurs when:
Force = 0
Displacement = 0
Force and displacement are perpendicular or form a 90º angle.
Energy
the ability to do work; property that must be transferred to an object to do work
Mechanical Energy
includes potential and kinetic energy
Potential Energy
energy that is formed due to the object’s position, orientation, or composition
Kinetic Energy
energy that is formed due to the object’s motion