Physics 121C Mechanics Lecture 10 Circular Motion October 25, 2004

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Physics 121C - MechanicsLecture 10Circular
MotionOctober 25, 2004

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Announcements

• Homework Assignment 4 is presently due on Tycho
  by 900 PM on Wednesday, October 27. However, it
  has not been posted yet, so the deadline will
  probably be extended.
• The grades for Exam 1 are now being processed.
  We hope to return the papers by Wednesday,
  October 27.
• On future exams, if you would like to be seated
  in a left-handed seat, or in a right-handed seat
  on an aisle, or at one of the two tables in the
  back, or on the front row, or towards the back of
  the room, send me E-mail stating such
  preferences. I will try to take them into
  account when making the next seating assignments.
  For each exam, the seat assigments will be
  posted on Tycho on the day before the exam.

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Lecture Schedule (Part 2)
You are here!
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A Particle inUniform Circular Motion
For a particle in uniform circular motion,
the velocity vector v remains constant in
magnitude, but it continuously changes its
direction.
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Angular Position q
The angular position q (in radians) that a
particle in makes with the coordinate axis x is
q s/r, where s is the arc length, i.e., the
length of the arc traced by the trajectory of the
particle as it moves from the x axis to its
current position. 0 q 2p. The
radians unit is actually dimensionless
(length/length), but serves to remind us that it
is an angle with a particular range of values.
The degree measure of angle, on the other hand,
is a true dimension that has to be used
appropriately.
s rq q s/r
10 (p/1800) rad 0.0174533 rad 1 rad
1800/p 57.2960
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Angular Velocity w

• The angular velocity w (in radians/s) is the
  speed with which the angle q changes as the
  particle moves in its circular path. Thus,
  wdq/dt.
• Another unit used for angular velocity is
  rpm (revolutions per minute). 1 rpm 2p
  radian/minute 2p/60 radians/s.
• It is conventional to treat q and w as
  quantities that have a sign. Before discussing
  such signs, we must check the coordinate system.
  If the direction from x to y is counterclockwise,
  the coordinate system is right-handed, which is
  standard. In a right-handed coordinate system
• If q increases counterclockwise, it is a
  positive angle.
• If w describes a counterclockwise rotation, it
  is a positive angular velocity.

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Example A Rotating Crankshaft
A 4.0 cm diameter crankshaft turns at 2400
rpm. What is the speed of a point on the surface
of the crankshaft?
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Graphical Representationof Circular Motion
This figure shows the angular position of a
particle moving around a circle of radius r.
Graph the angular velocity w of the particle.
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Clicker Question 1
A particle moves clockwise around a circle
at constant speed for 2.0 s. It then reverses
direction and moves counterclockwise at half the
original speed until it has traced trough the
same angle. Which graph shows the particles
angle vs. time?
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Example A Roulette Wheel
A small steel roulette ball rolls around the
inside of a 30 cm diameter roulette wheel. The
ball completes 2 rev in 1.20 s. What is the
balls angular velocity? What is the balls
position at t2.0 s? Assume qi0.
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Radial-Tangential Coordinates
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Radial and Tangential Velocity
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Acceleration inUniform Circular Motion
A particle moves with constant speed in a
circle. The length of the vector v is constant
but its direction changes. Therefore, the
acceleration vector a points inward toward the
center of the circular path. This is called
centripetal acceleration.
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Velocity and Acceleration
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Clicker Question 2
Which motion has the largest centripetal
acceleration?
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Dynamics ofUniform Circular Motion
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Example Spinning in a Circle
An energetic father places his 20 kg child
in a 5.0 kg cart to which is attached a 2.0 m
long rope. He then holds the end of the rope and
spins the cart and child in a circle, keeping the
rope parallel to the ground. If the tension
in the rope is 100 N, how many revolutions per
minute does the cart make?
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Clicker Question 3
A block on a string spins in a horizontal
circle on a frictionless table. Which tension is
the largest?
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Circular Orbits (1)
Thought Experiment On an airless planet,
cannon balls are shot from a cannon mounted on a
tower ar increasing muzzle velocities, and go
farther and farther as the velocity is
increased. What limits their range?
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Circular Orbits (2)
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End of Lecture 10

• Before the next lecture, read Knight,Chapters
  7.5 through 8.2
• Homework Assignment 4 should be submitted on
  the Tycho system by 900 PM, next Wednesday, Oct.
  27.(24 hours late Þ 70 credit)
• If you have not already done so, registeryour
  clicker athttp//faculty.washington.edu/jcramer/
  ph121c/Clicker