vm240 Introduction to Dynamics and Vibrations
Summer 2008
Exam # 1
May 20, 2008
Total Points = 100
1. (50 points) To manufacture sheets of nancomposite, students in ME450 designed a
“spin grower” in which the nancomposite is deposited onto a spinning turntable and
is distributed due to the kinetics of the spinning table.
Consider a small drop of
nanocomposite, of mass
m
, deposited onto the table, which is oriented horizontally
(gravity acts downward), as sketched below. The drop is deposited a distance
L
from
the center of the turntable. The turntable starts at rest and is given a constant angular
acceleration,
¨
θ
=
α
. The coefficient of static friction, between the nanocomposite drop
and the turntable, is given by
μ
.
a. Given the above data, and assuming that the nanocomposite does not slide on the
turntable, derive an expression for the acceleration vector of the nanocomposite
drop, with respect to a fixed inertial frame, as a function of time,
t
.
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 Fall '09
 Hulbert
 Force, Mass, nanocomposite drop

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