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40. Two balls with masses M and m are connected byrigid rod of length L and negligible mass as shown inFigure P10.40. For an axis perpendicular to the rod(a) show that the system has the minimum momentof inertia when the axis passes through the center ofmass. (b) Show that this moment of inertia is Г-, L2where umM/(m+ M)Figure P10.40

Question
40. Two balls with masses M and m are connected by
rigid rod of length L and negligible mass as shown in
Figure P10.40. For an axis perpendicular to the rod
(a) show that the system has the minimum moment
of inertia when the axis passes through the center of
mass. (b) Show that this moment of inertia is Г-, L2
where umM/(m+ M)
Figure P10.40
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40. Two balls with masses M and m are connected by rigid rod of length L and negligible mass as shown in Figure P10.40. For an axis perpendicular to the rod (a) show that the system has the minimum moment of inertia when the axis passes through the center of mass. (b) Show that this moment of inertia is Г-, L2 where umM/(m+ M) Figure P10.40

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Step 1

a)

Moment of Inertia for mass M is,

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Step 2

Total moment of Inertia is,

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Step 3

Differentiate the above equation w...

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Physics

Centre of Mass and Centre of Gravity

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