Moment of inertia of a cylinder

In summary, the task is to find the moment of inertia of a cylinder about its center of mass along the three principle axes, with the z axis being normal to the circular faces of the cylinder. The equation to be used is ∑miri2. The Izz value is easy to calculate, but the Iyy value requires a double integral and may be solved using the parallel axis theorem. If the moment of inertia for a disk around an axis through the center in its own plane is known, the double integral becomes a single integral.
  • #1
irishetalon00
18
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Homework Statement


Need to find the moment of inertia of a cylinder, about its center of mass, about the three principle axes. Z axis is normal to the circular faces of the cylinder. mass = M, radius = R, height = h

Homework Equations


∑miri2

The Attempt at a Solution


The Izz for whatever reason is trivial for me, easy to solve.
The Iyy = Ixx I'm having trouble with. I think it might be because this requires a double integral?
 
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  • #2
What relationships have you got available to tackle this ? Familiar with the parallel axis theorem ? If you have ##I## for a disk around an axis through the center in its own plane, then your double becomes a single ...
 

1. What is the formula for calculating the moment of inertia of a cylinder?

The formula for calculating the moment of inertia of a cylinder is I = 1/2 * mr^2, where I is the moment of inertia, m is the mass of the cylinder, and r is the radius of the cylinder.

2. How does the moment of inertia of a cylinder change with respect to its mass and radius?

The moment of inertia of a cylinder increases with both mass and radius. This is because the moment of inertia is directly proportional to the mass and the square of the radius.

3. What is the significance of the moment of inertia for a cylinder?

The moment of inertia of a cylinder is a measure of its resistance to rotational motion. It helps in determining how much force is needed to accelerate or decelerate the cylinder's rotational motion.

4. How does the moment of inertia of a hollow cylinder differ from that of a solid cylinder?

The moment of inertia of a hollow cylinder is greater than that of a solid cylinder with the same mass and radius. This is because the mass is distributed farther from the axis of rotation in a hollow cylinder, resulting in a larger moment of inertia.

5. How does the moment of inertia of a cylinder compare to that of other shapes?

The moment of inertia of a cylinder is lower than that of a sphere or a solid cylinder with the same mass and radius. This is because the mass is distributed closer to the axis of rotation in a cylinder, resulting in a smaller moment of inertia.

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