KINEMATICSKINEMATICS

is a branch of is a branch of dynamics which describes the which describes the motion

of objects without of objects without consideration of the consideration of the

circumstances leading to circumstances leading to the motion the motion

FRAME OF REFERENCEFRAME OF REFERENCE

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

- Coordinate axes are used to represent the frame of reference

Moving or Not Moving?Moving or Not Moving?

Click to play

Reference Frame Video

Motion depends on Motion depends on perspectiveperspective

Relativity.swf

SCALAR QUANTITYSCALAR QUANTITY- A quantity define by magnitude A quantity define by magnitude

onlyonly

(Ex) 5 meters (Ex) 5 meters

4 kg4 kg

50 kilometers per hour (kph)50 kilometers per hour (kph)

60 degrees60 degreestime, distance, speed, temperature, mass, energy

VECTOR QUANTITYVECTOR QUANTITY

A quantity that requires both A quantity that requires both magnitude and direction.magnitude and direction.

(Ex) 5 meters north (5 m N)(Ex) 5 meters north (5 m N)

35 km NNE35 km NNE

65 newtons to the left (65 N 65 newtons to the left (65 N left)left)

13 m/s down13 m/s downvelocity, displacement, force, momentum, electric and magnetic fields

DIRECTIONDIRECTIONSS

0

90

180

270

22.5 o W of N

67.5 o N of W

Vectors are usually named with capitalletters with arrows above the letter.

They are represented graphically as arrows.

The length of the arrow correspondsto 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

GRAPHICAL METHODGRAPHICAL METHOD The vectors are added using the head-The vectors are added using the head-

to-tail method. Magnitude can be to-tail method. Magnitude can be measured and the direction determined measured and the direction determined through the use of a protractorthrough the use of a protractor

(Ex.)(Ex.)

=

=

TRIGONOMETRIC TRIGONOMETRIC METHODMETHOD

Roman Road

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.

3

45

SOH

CAH

TOA

Resolving a Vector Into ComponentsResolving a Vector Into Components

+x

+y

A

Ax

Ay

The horizontal, or x-component, of A is found by Ax = A cos

The vertical, ory-component, of A is found by Ay = A sin By the Pythagorean Theorem, Ax

2 + Ay2 = A2.

Every vector can be resolved using these formulas, such that A is the magnitude of A, and 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 AdditionAnalytical Method of Vector Addition1. Find the x- and y-components of each vector.

Ax = A cos = Ay = A sin = Bx = B cos = By = B sin =Cx = C cos = Cy = C sin =

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

Rx =

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

Ry =

4. Use the Pythagorean TheoremPythagorean Theorem to find the magnitude of the resultant vector.Rx

2 + 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.

= = TanTan-1-1 RRyy/R/Rxx

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

NE(+,+)

NW(-,+)

SW

(-,-)SE

(+,-)

Θ = tan-1 opp = tan -1 11 = 45 o

adj 11

Θ

EFFECT OF WIND ON A EFFECT OF WIND ON A PLANE’S VELOCITYPLANE’S VELOCITY

RESULTANT VELOCITY OF A RESULTANT VELOCITY OF A CROSSWIND ON A PLANE’S CROSSWIND ON A PLANE’S

VELOCITYVELOCITY

EFFECT OF RIVER EFFECT OF RIVER CURRENT ON A CURRENT ON A

RIVERBOAT’S MOTIONRIVERBOAT’S MOTION