IUPhysicsP201F2009
Assignment 7b
Due at 11:00pm on Sunday, October 26, 2008
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Introduction to Moments of Inertia and Rotational Kinetic Energy
Description:
Conceptual questions about moment of inertia; several basic computational questions on moment of
inertia and kinetic energy for discrete mass distributions. (version for algebrabased courses)
Learning Goal:
To understand the definition and the meaning of moment of inertia; to be able to calculate the
moments of inertia for a group of particles; to relate moment of inertia to kinetic energy.
By now, you may be familiar with a set of equations describing rotational kinematics. One thing that you may have
noticed was the similarity between
translational
and
rotational
formulas. Such similarity also exists in dynamics and
in the workenergy domain.
For a particle of mass
moving at a constant speed
, the kinetic energy is given by the formula
. If we
consider instead a
rigid object
of mass
rotating at a constant angular speed
, the kinetic energy of such an object
cannot be found by using the formula
directly, since different parts of the object have different linear
speeds. However, they all have the same
angular
speed. It would be desirable to obtain a formula for kinetic energy
of rotational motion that is similar to the one for translational motion; such a formula would include the term
instead of
.
Such a formula can, indeed, be written: For rotational motion of a system of small particles or for a rigid object with
continuous mass distribution, the kinetic energy can be written as
.
Here,
is called the moment of inertia of the object (or of the system of particles). It is the quantity representing the
inertia with respect to rotational motion.
It can be shown that for a discrete system of
particles, the moment of inertia (also known as
rotational inertia
) is
given by
.
Page 1 of 27
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10/13/2008
http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1161385
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View Full DocumentIn this formula,
is the mass of the
i
th particle and
is the distance of that particle from the axis of rotation.
Part A
On which of the following does the moment of inertia of an object depend?
Check all that apply.
Unlike mass, the moment of inertia depends not only on the amount of matter in an object but also on the
distribution of mass in space
. The moment of inertia is also dependent on the
axis of rotation
. The
same
object, rotating with the
same
angular speed, may have
different
kinetic energy depending on the axis of
rotation.
ANSWER:
g
f
e
d
c
linear speed
g
f
e
d
c
linear acceleration
g
f
e
d
c
angular speed
g
f
e
d
c
angular acceleration
g
f
e
d
c
b
total mass
g
f
e
d
c
b
shape and density of the object
g
f
e
d
c
b
location of the axis of rotation
Part B
What is the moment of inertia
of particle a?
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 Spring '09
 physics
 Physics, Inertia, Assignment Print View, rotational kinetic energy

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