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PHCC 141: Physics for Scientists and Engineers I - Fall 2007
10b. Angular Dynamics
Due at 11:59pm on Monday, October 29, 2007
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Number of answer attempts per question is:
5
You gain credit for:
correctly answering a question in a Part, or correctly answering a question in a Hint.
You lose credit for:
exhausting all attempts or requesting the answer to a question in a Part or Hint, or incorrectly answering a question in a Part.
Late submissions:
reduce your score by 100% over each day late.
Hints
are helpful clues or simpler questions that guide you to the answer. Hints are not available for all questions. There is
no penalty
for leaving questions in Hints unanswered.
Grading of
Incorrect Answers
For
Multiple-Choice
or
True/False
questions, you lose
100%
/
(
# of options - 1
)
credit per incorrect answer.
For
any other
question, you lose 3% credit per incorrect answer.
Conservation of Angular Momentum
Record and Turntable
Learning Goal:
To understand how to use conservation of angular momentum to solve problems involving collisions of
rotating bodies.
Consider a turntable to be a circular disk of moment of inertia
rotating at a constant
angular velocity
around an axis through the center and perpendicular to the plane of the
disk (the disk's "primary axis of symmetry"). The axis of the disk is vertical and the disk is
supported by frictionless bearings. The motor of the turntable is off, so there is no external
torque being applied to the axis.
Another disk (a record) is dropped onto the first such that it lands coaxially (the axes
coincide). The moment of inertia of the record is
. The initial angular velocity of the second
disk is zero.
There
is
friction between the two disks.
After this "rotational collision," the disks will eventually rotate with the same angular velocity.
Part A
What is the final angular velocity,
, of the two disks?
Hint A.1
How to approach the problem
Because there is friction between the record and turntable, you can't use energy conservation. However, since there are no net
external torques acting on the system, angular momentum is conserved.
Part A.2
Initial angular momentum
Find the magnitude,
, of the (combined) initial angular momenta of the two disks.
Express
in terms of
,
, and/or
.
ANSWER:
=
Part A.3
Final angular momentum
Find the magnitude,
, of the (combined) final angular momenta of the two disks.
Express
in terms of
,
, and/or
.
ANSWER:
=
Express
in terms of
,
, and
.