INSTRUCTIONAL MEDIA

THE MOVEMENT WITH VEKTOR ANALYZE

COMPILED BYTUTI RESRI

YANTIRSA1C312017

LECTURER Drs.M.HIDAYAT,M.Pd.

THE MOVEMENT WITH VEKTOR ANALYZE

UNIT VECTOR

CIRCULAR MOTION

THE PARABOLIC MOTION

THE MOVEMENT WITH VEKTOR ANALYZE

Competition standart. Analysist of natural indication and regularity in scope mechanics point object.

BASIC COMPETENCE1.1 Analyze straight motion,

circular motion and using the parabolic motion vector.

RECTILINEAR MOTION ANALYSIS

DEFINITIONSMEANING OF MOTION

An object is said to move when they change the position of other objects that serve as a reference point.

Body is said stationary (not moving)position when the object was not changed to other property used as a reference point.

MOTION STRAIGHT. object-motion trajectory straight-called rectilinear motion. -straight motion of an object in everyday life generally irregular.

A. UNIT VECTOR

Y

Ayj

α x Ax i

Unit vector is a vector whose magnitude one, without force, its direction along the coordinate axes. For the Cartesian coordinate system, the unit vectors along the x-axis direction, y, and z.The components of a vector to the x and y axes, respectivelyAx = A cos α and Ay = A sin α.

ACCELERATION

POSITION VECTOR VELOCITY

1. position vector

The position of a car (A) of the reference point (O) can be expressed by a position vector (position vector), ie OA or r.r = x i+y j -> two-dimensionalLarge (long) position vector expressed

r = x i y j z k -> three dimensional

A

r = x i + y j

y j

x iO

Displacement experienced by the point A in the time interval t.r = r2 – r1

r = x i + y jLarge displacement can be written

Direction of movement of point A

As a function of time, the component vector

22 )()(r yx

x

y

tan

jir )()()( tytxt

2. VELOCITYSpeed : displacement of the object in a certain time interval.Average speed: position change interval divided

t

r

v

tx

x

vty

y

v

tz

z

v

The average speed equation

Large average speed

Directions average speed

kjiv zyx vvv

222zyx vvv v

x

y

v

vtan

INSTANTANEOUS VELOCITY : Velocity of object any given moment

The instantaneous velocity equation

The instantaneous velocity

Instantaneous velocity direction

dt

d

tv

rr

lim

dt

dxvx

dt

dyvy dt

dzvz

kjivdt

dz

dt

dy

dt

dx kjiv zyx vvv

222zyx vvv v

x

y

v

vtan

determine position of velocity function

On the z axis can be obtined in the same way

dt

dxvx dxdtvx

t

x

x

x

dtvdx00

t

x dtvxx0

0

t

x dtvxx0

0

t

y

y

y

dtvdy00

t

y dtvyy0

0

t

y dtvyy0

0

accalerationAcceleration: change of velocity per unit timea. Average acceleration: a change of pace once in a while

t

v

a

t

va xx

t

va yy

t

va zz

Average acceleration aquation :

The average acceleration :

Average acceleration direction

kjia zyx aaa

222zyx aaa a

x

y

a

atan

acceleration

b. instantaneous acceleration Instantaneous acceleration (a) is defined

as the average acceleration for the time interval approaches zero. Systematically, instantaneous acceleration is formulated as follows:

However, v = dr / dt to obtain

c. Determine velocity from acceleration function

On the z axis can be obtined in the same way

dt

dva xx

xx dvdta

t

x

v

v

x dtadv00

t

xxx dtavv0

0

t

xxx dtavv0

0

t

y

v

v

y dtadv00

t

yyy dtavv0

0

t

yyy dtavv0

0

acceleration

Parabolic motion

Blend motion trajectory uniform rectilinear motion in the horizontal direction (x-axis) with a uniformly accelerated motion in the vertical direction (y-axis) is called parabolic parabolic motion.

B

C

D

Evx=vo cos

vy=

vo s

in

Parabolic motion

At y axisAcceleration equation

GLBB velocity equation

Transfer equation

• At x axisVelocity equation

GLB transfer equation:cosox vv

tvx o cos

cos

xt

tavv oyy tgvv oy sin

2

2

1sin tgtvy o

2bxaxy

Parabolic motionWhen the bullet reaches its highest point, bullet velocity component in the vertical direction is zero or Vy = 0. thus at the highest point applies

so the time it takes a bullet to the highest point

substitution equation y in the equation of uniformly accelerated motion and bullet time required to produce the highest point of maximum height

with varying elevation angles will be obtained by varying the maximum height anyway. The maximum height is obtained if the elevation angle α = 90 °.Achieved the maximum horizontal distance defined by

C. ANALYZE OF CIRCULAR MOTION

CIRCULAR MOTION: motion trajectory of a circle.

x =

r s

in

r

vv

v

v

• ANGLE position

• angular velocityAverage angular velocity

Instantaneous angular velocity

the position of angle can determine too :

cosrx sinry

22 yxr x

ytan

12

12

ttt

dt

d

t

lim

t

dtt0

0 )(

• Angular acceleration

instantaneous angular acceleration

angular velocitu can determine too :

12

12

ttt

2

2

dt

d

dt

d

dt

d

t

dtt0

0 )(

CIRCULAR MOTION

Circular motion acceleration

Initial position

Acceleration of the object which always leads to the centre of the circle said centripetal acceleration.

t 0(t)

ar

va atau

2

o

v

v

v

CIRCULAR MOTION

In addition to centripetal acceleration, the change uniform circular motion there is also a tangential acceleration

Total acceleration possessed by objects that undergo uniform circular motion

rat

va TT

atau

sTtotal aaa

22sTtotal aaa

CIRCULAR MOTION

example

1. Kedudukan awal seekor kucing terletak pada r1 = 5i + 6j. Kemudian kucing bergerak sehingga kedudukannya berpindah ke posisi r2 = 5i + 2j. Perpindahan yang dialami kucing adalah....

A 4

B 5

C

D

E

7

9

25

SalahBenar!