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KINEMATICS

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KINEMATICS

is a branch of dynamics which describes the motion of objects without consideration of the circumstances leading to the motion

- a set of axes relative to which an observer can measure the position and motion of all points in a system, as well as the orientation of objects in it.
- Coordinate axes are used to represent the frame of reference

Click to play Reference Frame Video

- A quantity define by magnitude only
(Ex) 5 meters

4 kg

50 kilometers per hour (kph)

60 degrees

time, distance, speed, temperature, mass, energy

A quantity that requires both magnitude and direction.

(Ex) 5 meters north (5 m N)

35 km NNE

65 newtons to the left (65 N left)

13 m/s down

velocity, displacement, force, momentum,

electric and magnetic fields

22.5 o W of N

67.5 o N of W

0

90

270

180

Vectors are usually named with capital

letters with arrows above the letter.

They are represented graphically as arrows.

The length of the arrow corresponds

to the magnitude of the vector.

The direction the arrow points

is the vector direction.

Examples :

A = 20 m/s at 35° N of E

B = 120 m at 60° S of E

C = 5.8 m west

VECTOR ADDITION

GRAPHICAL METHOD

- The vectors are added using the head-to-tail method. Magnitude can be measured and the direction determined through the use of a protractor
(Ex.)

=

=

5

4

Roman Road

3

The secret of how Roman engineers were able to construct “straight as an arrow” roads is a piece of rope with 11 knots folded into three sections with the following ratio: 3:4:5.

SOH

CAH

TOA

Resolving a Vector Into Components

+y

The horizontal, or

x-component, of A is

found by Ax = A cos q.

A

Ay

q

Ax

+x

The vertical, or

y-component, of A is found by Ay = A sin q.

By the Pythagorean Theorem, Ax2 + Ay2 = A2.

Every vector can be resolved using these

formulas, such that A is the magnitude of A, and

q is the angle the vector makes with the x-axis.

Each component must have the proper “sign”

according to the quadrant the vector terminates in.

Analytical Method of Vector Addition

1.Find the x- and y-components of each vector.

Ax = A cos q =

Ay = A sin q =

By = B sin q =

Bx = B cos q =

Cx = C cos q =

Cy = C sin q =

Rx =

Ry=

2. Add the x-components.

This is the x-component (Rx) of the resultant.

3. Add the y-components.

This is the y-component (Ry) of the resultant.

4. Use the Pythagorean Theorem to find the

magnitude of the resultant vector.

Rx2 + Ry2 = R2

5. Find the reference angle by taking the inverse

tangent of the absolute value of the y-component

divided by the x-component.

q = Tan-1Ry/Rx

6. Use the “signs” of Rx and Ry to determine the

quadrant.

NW

NE

(-,+)

(+,+)

(-,-)

(+,-)

SW

SE

Θ

Θ = tan-1 opp = tan -1 11 = 45 o

adj 11