Units


SI 



Mass 
M 
kilogram 
kg 
slug 

Length 
L 
meter 
m 
feet 
ft 
Force 
F 

N 
pound 
lb 
Time 
T 
second 
s 
second 
sec 
Relation between units is based on the equation F=ma:
1 N = (1 kg) (1 m/s^{2})
1 lb= (1 slug) (1 ft/sec^{2} )
Example of calculating mass in _{ } 
Unit conversion:
l lb 
= 
4.4482 N 
1 slug 
= 
14.5938 kg 
1 ft 
= 
0.3048 m 
1 ft 
= 
12 in 
1 mile 
= 
5,280 ft 
1 kip 
= 
1,000 lb 
1 ton 
= 
2,000 lb 
Rounding numbers:
Round your final answers to 3 significant figures
_{ }
As a general rule for engineering problems, the data are seldom known with an accuracy greater than 0.2%. Therefore, it is usually appropriate to record parameters beginning with “1” with four digits and with three digits in all other cases, i.e., 40.2 m and 15.58 m.
Homogeneous Rule:
A + B = C
All terms in an equation must have the same dimensions.
Scalars and Vectors
Notation:

Book 
By hand 
Scalar 
a 
a 
Vector 
a (bold faced) 
a or _{} 
a^{2}+ b^{2 }= c^{2}
tan(q) = b/a
sin(q) = b/c
cos(q) = a/c
a+b+g=180^{o}
Sine law:
Cosine law:
o A line intersecting parallel lines:
Coordinates and Addition of Vectors
Unit vector: A vector of unit length
Components of a vector in orthogonal bases: Unit vectors i and j are along the x and y directions
Addition of vectors using the components:
Vectors in 3D
Unit vector: A vector of unit length.
Base vectors for a rectangular coordinate system: A set of three mutually orthogonal unit vectors
Right handed system: A coordinate system represented by base vectors which follow the righthand rule.
Rectangular component of a Vector: The projections of vector A along the x, y, and z directions are A_{x}, A_{y}, and A_{z}, respectively.
Magnitude of a Vector:
Direction Cosines: Cos(a), Cos(b), Cos(g)
Unit vector along a vector: The unit vector u_{A} along the vector A is obtained from
Addition of vectors: The resultant vector F_{R} obtained from the addition of vectors F_{1}, F_{2}, …, F_{n} is given by
Coordinates of points in space: The triplet (x,y,z) describes the coordinates of a point.
The vector connecting two points: The vector connecting point A to point B is given by
A unit vector along the line AB: A unit vector along the line AB is obtained from
A vector along AB: A vector F along the line AB and of magnitude F can be obtained from
The dot product: The dot product of vectors A and B is given by
Projection of a vector by using the dot product: The projection of vector A along the unit vector u is given by
Examples: