The figure below shows a system of four particles joined by light, rigid rods. Assume a = b and M is larger than m.
www.webassign.net/serpse8/10oq006.gif
1) About which of the coordinate axes does the system have the smallest moment of inertia?
a. x axis
b. y axis
c. z axis
d. The moment of inertia has the same small value for two axes
e. The moment of inertia is the same for all three axes.
2) About which of the coordinate axes does the system have the largest moment of inertia?
a. x axis
b. y axis
c. z axis
d. The moment of inertia has the same small value for two axes
e. The moment of inertia is the same for all three axes.
Explanations would be helpful!
4 Answers

The more mass the further from the axis of rotation, the greater the moment. Think about a mountain bike tire and wheel. The tire and rim are stronger and wider and therefore more massive. A 15/18 speed racing bike has very thin rims and tires that are far less massive. The racer’s wheels have a smaller moment.
1)a
2)c Rotation about the z axis has the most mass away from the axis – both blue M and both tan m masses. Rotation about the y axis has both blue M masses and rotation about the x axis only has the smaller m masses.
It is more difficult to accelerate a mountain bike but it will coast longer. Racers accelerate much faster but won’t coast as far. Obviously you can say the same thing about a heavier bike in general but wheel moments do make a difference.

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RE:
About which of the coordinate axes does the system have the smallest moment of inertia?
The figure below shows a system of four particles joined by light, rigid rods. Assume a = b and M is larger than m.
www.webassign.net/serpse8/10oq006.gif
1) About which of the coordinate axes does the system have the smallest moment of inertia?
a. x axis
b. y axis
c. z axis
d….

coordinate axes system smallest moment inertia

Correct Answers:
1) A
2) C