294 Rotation of a Rigid Object About a Fixed AxisP10.22IMx mLx=+−22afdIdxMxm L x=−−=220af(for an extremum)∴=+xmLMmdIdxmM22; therefore Iis minimum when the axis ofrotation passes through xmL=+which is also the centerof mass of the system. The moment of inertia about an axispassing through xismLmmLMmLLCM=+LNMOQP+−+LNMOQP=+=21µwhere =+Mm.xMmLL−xxFIG. P10.22Section 10.5Calculation of Moments of InertiaP10.23We assume the rods are thin, with radius much less than L.Call the junction of the rods the origin of coordinates, andthe axis of rotation the z-axis.For the rod along the y-axis, ImL=132from the table.For the rod parallel to the z-axis, the parallel-axis theoremgivesrmLmLFHGIKJ≅114222axis of rotationzxyFIG. P10.23
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .