Unformatted text preview: ass. Each such element of mass may be viewed as a
element
point mass with its individual position vector. Also, at the high school, we work with
easy examples where a crosssection of the solid is uniform about an axis or at least
symmetric about an axis.
The moment of iner tia I i s defined as the measure of the tendenc y to
tendency
m oment
t endenc
otate
r otate of a rigid body.
About an axis A : IA = the axial moment of iner tia.
a xial
About a point P : I P = the polar moment of iner tia.
p olar 193 y x (0,0) 43210987654321
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43210987654321 (0,0) 54321
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54321 y x lesser tendency to rotate about xaxis
tendency greater tendency to rotate about xaxis
tendency In the diagrams above the same brick of uniform density, depending on its
orientation
tendency
rota
otate
orienta tion , has a different tendenc y to r ota te o r moment of iner tia
t endenc
m oment
about the xaxis. It is impor tant to note that the brick is not in motion. The
brick is at rest or in a state of iner tia . Therefore the moment of iner tia
i ner
m oment
of a rigid body depends only on the orientation o r distance of the individual
o rientation
mas
elements of ma ss f rom the axis or point of rotation.
Measures may be formulated in different ways. Whatever be the measure, it
should give a sense and propor tion of the entity being measured. Thus the
formula for the moment of iner tia a bout an axis is defined as:
m oment
IA = (mass) . (square of perpendicular distance to the axis of rotation)
This has the advantage of taking into account the orientation without being
o rientation
affected by which side of the axis, negative or positive, the rigid body is
positioned or located. The quantity I c an be used directly in the equation
of the kinetic energy of rotation. The moment of iner tia is always a positive
m oment
quantity. The measure of the tendenc y to r otate does not specify or include
tendency rota
otate
t endenc
the direction of...
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 Fall '09
 TAMERDOğAN
 Limit, Δx

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