R'L' Sudduth

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Lecture 19
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SEEM to be very different, BUT they have the same
free body diagram . . .
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Orbital Motion is Projectile Motion!
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Orbiting projectile is in free fall
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A Peek Ahead
Keplers Law
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Orbit Radius R
Johannes Kepler
Orbital Period T
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A car is passing over the top of a hill at speed
v. At this instant,

• 1 n gt w
• 2 n w
• 3 n lt w
• 4 Cant tell without knowing v

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y
x
x
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Full Disclosure
mg
N
N
N
N
a
mg
mg
a
mg
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Non-Uniform Circular Motion
Tangential Acceleration
Radial (centripetal) Acceleration
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Dynamics of Non-Uniform Circular Motion
Just Newtons Second Law . . .
special case at constant
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Non-Uniform Circular Motion constant at
angular acceleration
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On the motion diagram, the red arrows show the
radial acceleration at four sequential points of
circular motion. On the path from point 2 to
point 3, the average tangential acceleration is
3
1

• zero
• positive
• negative
• not enough information to tell

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An airplane is flying in a horizontal circle at a
speed of 482 km/h. The wings of the plane are
tilted at 38.2? to the horizontal. Find the
radius of the circle in which the plane is
flying. Assume that the centripetal force is
provided entirely by the lift force perpendicular
to the wing surface.
1 2.3 km
4 5.3 km
2 3.8 km
5 1.4 km
3 0.5 km
6 none of the above
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R
R
H
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In the previous problem, the tangential
acceleration is constant. What about the radial
acceleration?
The radial acceleration decreases as the particle
slows down.
Does the analysis we have performed apply to a
particle projected with initial speed v0 up a
frictionless circular ramp?
No!
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n
mg
The angular acceleration is not constant as the
motion proceeds. The simple kinematic formulae
cannot be used.
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Aside Using energy principles, this problem can
be solved in two steps without calculus!
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A block slides around a circle of radius R on a
rough table top. What is the linear velocity of
the block after it has traced out ¾ of its
circular trajectory?
v0 7 m/s
R 2m
Top View
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• What time does the Duke game start?
• 900 pm
• 800 pm
• 700 pm
• 730 pm
• 630 pm