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Ph 111
NAME ________RWB
_______________________
November 5, 2008
Quiz 4 Solutions
Please give your numerical answers to at least three significant figures.
Please give the correct units (m/s, kg,
rad/s, hour, day, etc.) with each answer.
Problem 1.
Two turtles, each of mass M = 2.4 kg, sit on an approximately massless branch in the water.
They
sit on opposite sides of the center, each a distance R = 1.4 m from the center of the branch.
(a)
What is the moment of inertia of the system of branch and two turtles, about the center of the branch?
Just MR
2
for each turtle:
()
(
)
2
22
2
2 2.4 kg 1.4 m
9.408 kgm
IM
R
==
=
(b)
Suppose that the branch is initially rotating at a rate of
ω
= 0.34 radians/sec.
Then two more identical
turtles, with the same mass as the others,
jump onto the branch, right next to the turtles already there.
The new
turtles are not moving when
they jump onto the branch.
What is the new angular rate of rotation?
Conservation of angular momentum says
before
before
after
after
LI
I
The moment of inertia doubles; so the
angular velocity is reduced by a
factor of 1/2.
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