The moment of inertia of a cylinder depends on its mass distribution and the axis of rotation. The moment of inertia is a measure of an object's resistance to changes in its rotational motion.
If the axis of a cylinder is doubled along its diameter, the moment of inertia will change. The moment of inertia of a solid cylinder is given by the formula:
I = (1/2) * m * r^2,
where I is the moment of inertia, m is the mass of the cylinder, and r is the radius of the cylinder.
When the axis of the cylinder is doubled along its diameter, it means that the radius (r) of the cylinder becomes half of what it was before. Let's say the original radius was r1. After doubling the axis, the new radius will be r2 = r1/2.
Plugging this new radius value into the formula, we get:
I2 = (1/2) * m * (r1/2)^2 = (1/2) * m * (1/4) * r1^2 = (1/8) * m * r1^2.
Comparing the new moment of inertia (I2) to the original moment of inertia (I1), we find that:
I2 = (1/8) * I1.
So, when the axis of a cylinder is doubled along its diameter, the moment of inertia decreases to one-eighth (1/8) of its original value. This means that the cylinder becomes easier to rotate around its new axis of rotation compared to its original axis.