The three masses shown in the figure are connected by massless, rigid rods.&nbsp;Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page. Express your answer to two significant figures and include the appropriate units.&nbsp;Find the moment of inertia about an axis that passes through masses B and C.

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The three masses shown in the figure are connected by massless, rigid rods.&amp;nbsp;Find the moment of inertia about an axis that passes through mass A and is perpendicular to the page. Express your answer to two significant figures and include the appropriate units.&amp;nbsp;Find the moment of inertia about an axis that passes through masses B and C.

sirpsta3u · Accepted Answer

Step 1&amp;nbsp;Moment of inertia is a rotational analogue of mass, it is also known as rotational inertia..&amp;nbsp;moment of inertia about an axis is given as&amp;nbsp;1)&amp;nbsp;I=MR&amp;nbsp;where R is the mass&#039;s distance from the rotational axis.&amp;nbsp;M is the mass of the object&amp;nbsp;Step 2&amp;nbsp;The masses B and C lies at a distance of 10 cm from mass A.&amp;nbsp;Moment of inertia of the system about an axis passing through A and perpendicular to the page is&amp;nbsp;I=(100×102)+(100×102)&amp;nbsp;=2.0×104gcm2&amp;nbsp;Consider that A is separated from the axis by a.102=a2+62&amp;nbsp;a=102−6=8cm&amp;nbsp;Moment of inertia of the system about an axis passing through B and C, since B and C lies on the axis, there is no contribution of them to MI&amp;nbsp;I=200×64=1.28×104gcm2&amp;nbsp;Step 3&amp;nbsp;Moment of inertia of the system about an axis passing through A and perpendicular to the page is&amp;nbsp;2.0×104gcm2&amp;nbsp;Moment of inertia of the system about an axis passing through B and C is&amp;nbsp;1.28×104gcm2

Lynne Trussell · Accepted Answer

Step 1  x-coordinate of the center of mass;  ссxcm=m1x1+m2x2+сs˙+mnxnm1+m2+сs˙+mn  Similarly, y-coordinate of the center of mass:  ссycm=m1y1+m2y2+сs˙+mnynm1+m2+сs˙+mn  Moment of inertia:  I=mr2  Coordinates of the 200g mass is  x-coordinate =122=6cm  y-coordinate =102−62=8cm  xcm=(100)(0)+(200)(0)+(200)(8)100+100+200  xcm=4cm  The x-coordinate of the center of mass is 4 cm.  Step 2  ycm=(100)(0)+(200)(0)+(200)(8)100+100+200  ycm=4cm  The y-coordinate of the center of mass is 4 cm  Step 3  From the second equation:  I=mBrB2+mcrc2=(100×10−3)(10×10−2)2+(100×10−3)(10×10−2)2  I=2.0×10−3kg×m2  The moment of inertia about an axis that passes through mass  A and is perpendicular to the page is 2.0×10−3kg×m2  Step 4  I=mArA2=(200×10−3)(8×10−2)2=1.28×10−3kg×m2  The moment of inertia about an axis that passes through  masses B and C is 1.28×10−3kg×m2

The three masses shown in the figure are connected by massle

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