Younes Sina's Lecture at Pellissippi State Community College

1. Chapter One:
Units, Vectors, and Trigonometry

2. Fundamental Units Area
A=L2
Volume
V=L3
Velocity
V=L/T
Acceleration
a=v/T=L/T2
s Length
L
Time
T
1 m 1 s
1 m 1 s
g 1 ft 1 s
m
Slug)
1 ft 1 s

3. A Fundamental Units Table of Units

4. Units

5. A B
6 mi and 551 yd
? m

9. Solution: F = Ma; F = (4.0kg)(3.5m/s2) = 14
kgm/s2 = 14 N
w = Mg ; w = (5.0kg)(9.8 m/s2) = 49N ; therefore, the magnitude of N is also 49N.

10. Solution:
In the vertical direction, gravity pulls the block down by the weight
force, w =Mg = 98N, and the surface pushes it up with an equal and
opposite force of N = 98N as well.
In the horizontal direction, the applied force F = Ma acts to the
left. F = (10.kg)( 4.0m/s2) = 40.N (to the left)

11. Vectors
A scalar quantity requires a magnitude only. Examples
are: mass, volume, and temperature.
A vector quantity requires a magnitude as well as a
direction. Examples are: velocity, acceleration, and force.
Arrows are used to show vectors.
The length of the arrow represents the magnitude and
the angle it makes with a reference axis counts as
its direction. The reference axis is usually chosen to be
the positive x-axis.

13. Addition of Vectors:
The addition of vectors is very easy. There are two cases.
Case I ) Parallel vectors:

14. Example 6: Draw the following vectors: A = (5.0N,
30.0o), B = (10.0N, 70.0o), C = (8.0N, 230.0o), and D =
(8.0N, -130.0o).
Solution: Note that counterclockwise (CCW) is positive for
angles and clockwise (CW) is negative. On a set of x-y
coordinates system, select the 30.0o 70.0o230.0o and -
130.0oangles as shown and using an appropriate scale (1cm
= 1N, for example) mark appropriate lengths on the
corresponding lines. Another point to consider is that bold
letters are used to show vectors and regular letters to show
magnitudes. Finally, in this example, vectors C and D have
the same direction and magnitude and are therefore
equal. +230.0oand -130.0ospecify the same direction.

15. Example 7: From Point P(3,2) draw vector B equal
to A = (5.0m/s, 120o) that is drawn from the origin.
Solution: First draw a tiny x-axis from P. Then select a
120oangle from P by a line segment as shown, and then
select a length that represents 5.0m/s based on the scale
used.

16. Example 8: Draw A = (3.0 m/s2, 27o) from the origin and then -
A from point Q(2, 6).
Solution: First draw a line at 27othat passes through the origin
and select 3.0in. or 3.0cm on it depending on your choice of
scale. Next, locate point Q and draw another line through it
parallel to A. Finally select 3.0in. or 3.0cm on it but in the
opposite direction of A. Complete the arrowhead and label it -A.
Note that the direction of -A is (+/-) 180odifferent from that of A.

19. Trigonometry

25. Find the third side

28. Case II ) Non-Parallel Vectors:

31. 2) Analytical Method:

32. Example 17:
Given A = (4N, -30o)
and B = (8N, 70o) ,
find R = A + B by calculation.
Use the parallelogram method for
its graphical part.

35. A=5 m
B=2.1 m
C=0.5 m