Ch8-2 Kinematic

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Summary Three Coordinates (Tool)
Velocity
Acceleration
Reference Frame
Reference Frame
Path
Path
x
x
y
r
Observers measuring tool
y
r
O
Observer
Observer
(x,y) coord
(n,t) coord velocity meter
(r,q) coord
r
q
2
Choice of Coordinates
Velocity
Acceleration
Reference Frame
Reference Frame
Path
Path
x
x
y
r
Observers measuring tool
y
r
O
Observer
Observer
(x,y) coord
(n,t) coord velocity meter
(r,q) coord
r
q
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4
Translating Observer
Two observers (moving and not moving) see the
particle moving the same way?
Translating-only Frame will be studied
today
No!
Path
Observers Measuring tool
Which observer sees the true velocity?
Observer B (moving)
(x,y) coord
A
both! Its matter of viewpoint.
This particle path, depends on specific
observers viewpoint
(n,t) coord velocity meter
relative absolute
Observer O (non-moving)
Point if O understand Bs motion, he can
describe the velocity which B sees.
r
(r,q) coord
q
Two observers (rotating and non rotating) see the
particle moving the same way?
No!
translating rotating
Rotating axis will be studied later.
Observer (non-rotating)
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2/8 Relative Motion (Translating axises)

• Sometimes it is convenient to describe motions
  of a particle relative to a moving reference
  frame (reference observer B)

• If motions of the reference axis is known, then
  absolute motion of the particle can also be
  found.

• A a particle to be studied

• B a (moving) observer

Reference frame O
Reference frame B

• Motions of A measured by the observer at B is
  called the relative motions of A with respect to
  B

• Motions of A measured using framework O is
  called the absolute motions

• For most engineering problems, O attached to the
  earth surface may be assumed fixed i.e.
  non-moving.

frame work O is considered as fixed
(non-moving)
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Relative position

• If the observer at B use the x-y coordinate
  system to describe the position vector of A we
  have

Y

• Here we will consider only the case where the x-y
  axis is not rotating (translate only)

X
other coordinates systems can be used e.g.
n-t.
7
Relative Motion (Translating Only)

• x-y frame is not rotating (translate only)

y
Y
Direction of frames unit vectors do not change
x
0
X
Notation using when B is a translating frame.
Note Any 3 coords can be applied to Both 2
frames.
0
8
Understanding the equation
Path
Translation-only Frame!
Observer B
A
O B has a relative translation-only motion
This particle path, depends on specific
observers viewpoint
Observer O
reference framework O
reference frame work B
Observer B (translation-only Relative velocity
with O)
Observer O
Observer O
This is an equation of adding vectors of
different viewpoint (world) !!!
9
The passenger aircraft B is flying with a linear
motion to theeast with velocity vB 800 km/h. A
jet is traveling south with velocity vA 1200
km/h. What velocity does A appear to a passenger
in B ?
10
Translational-only relative velocity
You can find v and a of B
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Is observer B a translating-only observer
B
relative with O
Yes
Yes
O
Yes
No
?
13
To increase his speed, the water skier A cuts
across the wake of the tow boat B, which has
velocity of 60 km/h. At the instant when
? 30, the actual path of the skier makes an
angle ? 50 with the tow rope. For this
position determine the velocity vA of the skier
and the value of
Relative Motion (Cicular Motion)
Consider at point A and B as r-? coordinate
system
30
A
A
o
o
B
B
30
D
?
?
O.K.
M
Point Most 2 unknowns can be solved with 1
vector (2D) equation.
14
2/206 A skydriver B has reached a terminal speed
. The airplane has the
constant speed and is
just beginning to follow the circular path shown
of curvature radius 2000 m Determine (a) the
vel. and acc. of the airplane relative to
skydriver. (b) the time rate of change of the
speed of the airplane and the radius of
curvature of its path, both observed by
the nonrotating skydriver.
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(b) the time rate of change of the speed
of the airplane and the radius of curvature
of its path, both observed by the nonrotating
skydriver.
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