Units 

 

 

SI

 

U.S.

 

Mass

M

kilogram

kg

slug

 

Length

L

meter

m

feet

ft

Force

F

Newton

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/s2)

            1 lb= (1 slug) (1 ft/sec2 )

 

Example of calculating mass in U.S. system: The mass, m, of a particle which weighs W=10 lb and is in a gravitational field of with an acceleration of gravity g=32.2 ft/sec2 is 

 

 

 

 

 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  

 

a2+ b2 = c2

tan(q) = b/a

sin(q) = b/c

cos(q) = a/c

a+b+g=180o

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 3-D

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 right-hand rule.

Rectangular component of a Vector: The projections of vector A along the x, y, and z directions are Ax, Ay, and Az, respectively.

Magnitude of a Vector:

Direction Cosines: Cos(a), Cos(b), Cos(g)

Unit vector along a vector: The unit vector uA along the vector A is obtained from

Addition of vectors: The resultant vector FR obtained from the addition of vectors F1, F2, , Fn 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 A-B: A unit vector along the line A-B is obtained from

A vector along A-B: A vector F along the line A-B 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: