Free Fall:

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Physics 1710 Chapter 4 2-D MotionII
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• Free Fall
• Kinematics in two (or more) dimensions obeys the
  same 1- D equations in each component
  independently.

ax 0
y yinitial ½ gt 2
x xinitial vx,initial t
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Physics 1710 Chapter 4 2-D MotionII
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• Kinematic Equations

x(t) xinitial vinitial t 1/2 ao t 2 v(t)
dx/dt vinitial ao t a dv/dt ao
Observe Air Track
REVIEW
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Physics 1710 Chapter 4 2-D MotionII
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• 1' Lecture
• The velocity and acceleration of a body in a
  moving (and accelerating) frame of reference (FoR
  ) is equal to that of a stationary FoR minus the
  velocity or acceleration of the moving FoR.
• v ' v vframe of reference
• a ' a aframe of reference
• Motion in a circle at a constant speed is due to
  an acceleration toward the center of the circle,
  a centripetal acceleration of
• a - ?2 r and a v 2/ r toward the
  center.

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Physics 1710 Chapter 4 2-D MotionII
Physics 1710 Chapter 4 2-D MotionII
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• Frame of Reference

v v' vframe of reference and v' v - vframe
of reference
v
v'
vframe of reference
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Physics 1710 Chapter 4 2-D MotionII
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• Relative Motion
• and the Galilean Transformation
• r ' r vframe of reference t
• d r '/dt d r/dt vframe of reference
• v ' v vframe of reference
• d v '/dt d v/dt d vframe of reference/dt
• a ' a aframe of reference

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Physics 1710 Chapter 4 2-D MotionII
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• Relative Motion in a Free Falling Frame of
  Reference

In Lab Frame
In Moving Frame
a ' a aframe of reference
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Physics 1710 Chapter 4 2-D MotionII
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• Everyday Physics
• When a bird is flying at the same velocity(same
  speed and direction) as a car what is its
  relative velocity v' to the car?
• When you brake an automobile, which direction is
  the acceleration on the vehicle? Which direction
  do the passengers sense as the acceleration
  relative to the frame of reference of the car?

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Physics 1710 Chapter 4 2-D MotionII
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• Relative Motion
• and the Galilean Transformation
• v ' v vframe of reference
• a ' a aframe of reference

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Physics 1710 Chapter 4 2-D MotionII
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• Uniform Circular Motion

d ?/dt ? constant
x R sin ? y R cos ? R2 x2 y2 r (x,y)
x i y j
v
?
r
vx R cos ? d ?/dt R? cos ? vy - R sin ?
d ?/dt - R? sin ?
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Physics 1710 Chapter 4 2-D MotionII
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• Uniform Circular Motion

vx R cos ? d ?/dt R ? cos ? vy - R sin
? d ?/dt - R ? sin ?
v
?
ax - R ?2 sin ? ay - R ?2 cos ? a - ?2
r a v2/R, toward center
r
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Physics 1710 Chapter 4 2-D MotionII
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• Uniform Circular Motionin review
• ?a? a,
• a constant value always pointing toward the
  center of the circle Centripetal acceleration.
• a ax i a y j - ?2 r
• where
• ax a sin ? - (v2/R) sin ? - ?2 R sin ?
• ay a cos ? - (v2/R) cos ? - ?2 R cos ?

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Physics 1710 Chapter 4 2-D MotionII
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• Uniform Circular Motion
• a v 2 /R, toward center
• The Centripetal acceleration, where v is the
  tangential speed and R is the radius of the
  circle.
• v ? R 2pR / T ,
• Where T is the period or time to make one
  revolution.
• a 4p 2R/ T 2 ?2 R

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Physics 1710 Chapter 4 2-D MotionII
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• Uniform Circular Motion
• Little Johnny on the Farmpart II

?
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Physics 1710 Chapter 4 2-D MotionII
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• Uniform Circular Motion

In Frame of Reference of Bucket a' -g aFoR
- g
aFoR

If aFoR ? g In same (down) direction,a' is
up!
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Physics 1710 Chapter 4 2-D MotionII
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• Uniform Circular Motion

a (2p/T)2 R, T 1. sec R 1. m 2p 6. a
(6./1.sec)2 (1.m) a 36. m/sec 2 agt 3 g
g
a
Do you believe this?
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Physics 1710 Chapter 4 2-D MotionII
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• 80/20 Summary
• In a moving or accelerating Frame of Reference
• v ' v vframe of reference
• a ' a aframe of reference
• The Centripetal acceleration is
• a - ?2 r or a v 2/ r, toward the
  center.