Final answer:
To calculate the moment of inertia of a solid cylinder about an arbitrary axis using the parallel axis theorem, determine the moment of inertia for the center of mass, then add the product of the mass and the square of the distance from the center to the new axis.
Step-by-step explanation:
The question asks how to determine the moment of inertia of a solid cylinder about a specific axis using the parallel axis theorem.
To find the moment of inertia of a cylinder about its center of mass (ICM), we use the formula ICM = (1/2)MR², where M is the mass of the cylinder and R is its radius. To determine the moment of inertia about an arbitrary axis parallel to the central axis, we use the parallel axis theorem: I = ICM + Md², where d is the distance from the center of mass to the new axis.
For example, if we have a cylinder of mass M and radius R, and we want to find the moment of inertia about an axis through a point on the surface, we use the distance from this axis to the center of mass, which in this case is R (the radius). Therefore, I = (1/2)MR² + MR², simplifying to I = (3/2)MR². This calculation shows that the moment of inertia increases when the axis of rotation is moved away from the center of mass.