March 26, 2017

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Four identical particles, each with mass m, are arranged in the x,y plane like a cross. They are connected by light sticks to form a rigid body. If m=2.0kg and a=1.0 m the rotational inertia of this array about the y axis is:

I know that
I= mr^2
I=2 kgm^2 for one body
for 4 x 2.=8
so I figured if is a rigid body all the mass would count for the Y axis array, I am not sure.

Consider four objects, each having the same mass and radius
1) a solid sphere
2) a hollow sphere
3) a flat disk in the x,y plane
4) a hoop in x,y plane
The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis.

I know that rotational inertia is smaller when mass is closer to the axis so I throught

1, solid sphere has mass distributed close to axis
3) a flask disk would have a mass closely ditributed to its axis
2) a hollow sphere would have points where the mass was distributed close to the axis near the top
4) the hoop contains only a ring of mass and may not be near the axis.

The first is right, if the rotational axis is the z axis, perpendicular to the xy plane. But about the y axis, you only have the two x masses rotating.

I would reverse 2,3 on inertia. The hollow sphere will have more near the axis than the flat disk.

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