alittlebitofcalculus-pdf-january2011-111112001007-phpapp01

Let us 12 find the moment of inertia about the y axis

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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 cross-section 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 43210987654321 43210987654321 43210987654321 43210987654321 (0,0) 54321 54321 54321 54321 54321 54321 54321 54321 54321 54321 54321 54321 54321 54321 y x lesser tendency to rotate about x-axis tendency greater tendency to rotate about x-axis 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 x-axis. 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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