Physics 2211, Spring 2005

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Physics 2211 Lecture 16

• Circular Orbits
• Fictitious forces
• Non-Uniform Circular Motion

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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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Fictitious forces in Non-Inertial Frames of
Reference
A car and driver move a constant speed. Suddenly,
the driver brakes
Outside observer if the seat is
frictionless, the driver continues forward at
constant speed and collides with the front
window.
Inside observer a force F throws the driver
against the front window.
F
F is fictitious the observer is in a
non- inertial (accelerated) frame where Newtons
laws do not apply. There is no true push or
pull from anything.
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Fictitious forces in Non-Inertial Frames of
Reference

• Car turns
• Book continues on straight line
• In drivers reference frame,
• apparent (fictitious) force moves book
• across the bench seat

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A car is passing over the top of a hill at
(non-zero) 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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3
A ball on a string swings in a vertical circle.
The string breaks when the string is horizontal
and the ball is moving straight up. Which
trajectory does the ball follow thereafter?
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4
1
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Roller-Coaster
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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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R
R
H
v0
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In the previous problem, the tangential
acceleration is constant. What about the radial
acceleration?
R
v2
v1
The radial acceleration decreases as the particle
slows down.
v0
Suppose the rigid rod is removed does the
analysis of the previous example apply to a block
projected with initial speed v0 up a frictionless
circular ramp?
No, a is no longer constant!
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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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2
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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38.2o