INSTRUCTIONAL MEDIA
THE MOVEMENT WITH
VEKTOR ANALYZE
LECTURER Drs.M.HIDAYAT,M.Pd.
COMPILED BY
TUTI RESRI
YANTI
RSA1C312017
THE MOVEMENT WITH
VEKTOR ANALYZE
UNIT
VECTOR

THE
PARABOLIC
MOTION
CIRCULAR
MOTION
THE MOVEMENT WITH VEKTOR
ANALYZE
Competition standart
. Analysist of natural indication and
regularity in scope mechanics ...
RECTILINEAR MOTION ANALYSIS







DEFINITIONS
MEANING OF MOTION
An object is said to move when they change the
positi...
A. UNIT VECTOR
Unit vector is a vector whose
magnitude one, without
force, its direction along the
coordinate axes. For th...
1. position vector
The position of a car (A) of
the reference point (O) can
be expressed by a position
vector (position ve...
Displacement experienced by
the point A in the time interval
t.
r = r2 – r1
r= xi+ yj
Large displacement can be
written
r
...
2. VELOCITY

Speed​​: displacement of the
object in a certain time
interval.Average speed:
position change interval
r
divi...
INSTANTANEOUS VELOCITY : Velocity of object
r dr
any given moment
v lim

dx
dt

vx

t

dt

dy
dt

vy

The instantaneous ve...
determine position of velocity function
dx
dt

vx
x

v x dt
y

t

dx

dx
t

vx dt

x0

0

dy

v y dt

y0

0

t

x x0

t

v...
accaleration
Acceleration: change of
velocity per unit time
a. Average acceleration: a
change of pace once in a
while

a

...
acceleration





b. instantaneous acceleration
Instantaneous acceleration (a) is defined as
the average acceleration f...
acceleration
c. Determine velocity from acceleration
function
dvx
ax
a x dt dvx
dt
v

v

t

dvx
v0

t

dv y

a x dt
v0

0
...
Parabolic motion

vy=vo sin

Blend motion trajectory uniform rectilinear
motion in the horizontal direction (x-axis)
with ...
Parabolic motion
• At x axis
Velocity equation

vx

vo cos

GLB transfer equation:
x

vo cos

t

x
cos

t

At y axis
Accel...
When the bullet reaches
its highest point, bullet
velocity component in the
vertical direction is zero or
Vy = 0. thus at ...
C. ANALYZE OF CIRCULAR MOTION
CIRCULAR
MOTION: motion
trajectory of a
circle.

v

x = r sin

v

v

v

r
• ANGLE position

y

x r cos
r

x2

r sin

tan

y2

• angular velocity
Average angular velocity
2

t

y
x

1

t 2 t1

Inst...
CIRCULAR MOTION
v

Circular motion
acceleration
(t)

0

t

Initial position

v2
a
atau a
r

Acceleration of the
object whi...
CIRCULAR MOTION
In addition to centripetal acceleration, the
change uniform circular motion there is also
a tangential acc...
example
1. Kedudukan awal seekor kucing terletak pada
r1 = 5i + 6j. Kemudian kucing bergerak sehingga
kedudukannya berpind...
The motion with vector analyze
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The motion with vector analyze

  1. 1. INSTRUCTIONAL MEDIA THE MOVEMENT WITH VEKTOR ANALYZE LECTURER Drs.M.HIDAYAT,M.Pd. COMPILED BY TUTI RESRI YANTI RSA1C312017
  2. 2. THE MOVEMENT WITH VEKTOR ANALYZE UNIT VECTOR THE PARABOLIC MOTION CIRCULAR MOTION
  3. 3. THE MOVEMENT WITH VEKTOR ANALYZE Competition standart . Analysist of natural indication and regularity in scope mechanics point object. BASIC COMPETENCE 1.1 Analyze straight motion, circular motion and using the parabolic motion vector.
  4. 4. RECTILINEAR MOTION ANALYSIS     DEFINITIONS MEANING 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.
  5. 5. A. UNIT VECTOR 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, respectively Ax = A cos α and Ay = A sin α. POSITION VECTOR Y Ayj α VELOCIT Y x Ax i ACCELERA TION
  6. 6. 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 -> twodimensional Large (long) position vector expressed r = x i y j z k -> three dimensional A yj r=xi+yj O xi
  7. 7. Displacement experienced by the point A in the time interval t. r = r2 – r1 r= xi+ yj Large displacement can be written r ( x) 2 ( y ) 2 Direction of movement of point A y tan x As a function of time, the component vector r(t ) x(t )i y(t ) j
  8. 8. 2. VELOCITY Speed​​: displacement of the object in a certain time interval.Average speed: position change interval r divided v t y x vx vy z vz t t t The average speed equation v vx i v y j vz k Large average speed 2 2 v vx vy vz Directions average vy speed tan vx 2
  9. 9. INSTANTANEOUS VELOCITY : Velocity of object r dr any given moment v lim dx dt vx t dt dy dt vy The instantaneous velocity equation dx dy dz v i j k v vx i dt dt dt The instantaneous velocity v vx 2 vy 2 vz 2 Instantaneous velocity direction tan vy vx vz dz dt v y j vz k
  10. 10. determine position of velocity function dx dt vx x v x dt y t dx dx t vx dt x0 0 dy v y dt y0 0 t x x0 t vx dt y y0 v y dt 0 t x 0 t x0 vx dt 0 y y0 v y dt 0 On the z axis can be obtined in the same way
  11. 11. accaleration Acceleration: change of velocity per unit time a. Average acceleration: a change of pace once in a while a ax v t vy vx ay t t az vz t Average acceleration aquation : a ax i a y j azk The average acceleration : 2 2 a ax ay az Average acceleration direction tan ay ax 2
  12. 12. 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
  13. 13. acceleration c. Determine velocity from acceleration function dvx ax a x dt dvx dt v v t dvx v0 t dv y a x dt v0 0 a y dt 0 t t vx v0 x ax dt vy v0 y a y dt 0 t vx 0 t v0 x ax dt 0 vy v0 y a y dt 0 On the z axis can be obtined in the same way
  14. 14. Parabolic motion vy=vo sin 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. C B D E vx=vo cos
  15. 15. Parabolic motion • At x axis Velocity equation vx vo cos GLB transfer equation: x vo cos t x cos t At y axis Acceleration equation  GLBB velocity equation vy voy at vy vo sin Transfer equation y y vo sin t 1 2 gt 2 2 ax bx gt
  16. 16. When 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 Parabolic motion 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
  17. 17. C. ANALYZE OF CIRCULAR MOTION CIRCULAR MOTION: motion trajectory of a circle. v x = r sin v v v r
  18. 18. • ANGLE position y x r cos r x2 r sin tan y2 • angular velocity Average angular velocity 2 t y x 1 t 2 t1 Instantaneous angular velocity lim t d dt the position of angle can determine too : t (t ) dt 0 0 CIRCULAR MOTION • Angular acceleration 2 t 1 t 2 t1 instantaneous angular acceleration 2 d d dt dt d dt 2 angular velocitu can t determine too : (t ) dt 0 0
  19. 19. CIRCULAR MOTION v Circular motion acceleration (t) 0 t Initial position v2 a atau a r Acceleration of the object which always leads to the centre of the circle said centripetal acceleration. o v v
  20. 20. CIRCULAR MOTION In addition to centripetal acceleration, the change uniform circular motion there is also a tangential acceleration v atau aT t aT r Total acceleration possessed by objects that undergo uniform circular motion atotal aT as atotal aT 2 as 2
  21. 21. 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 7 D 9 E 25 Salah Benar!
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