What is the moment of inertia of a solid cylinder of mass M and radius R about its central axis?

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Q: What is the moment of inertia of a solid cylinder of mass M and radius R about its central axis?

Solution: The moment of inertia of a solid cylinder about its central axis is given by I = 1/2 MR^2.

Steps: 6

Step 1: Understand what moment of inertia means. It is a measure of how difficult it is to change the rotation of an object.
Step 2: Identify the shape of the object. In this case, we have a solid cylinder.
Step 3: Recognize that the moment of inertia depends on the mass and the distribution of that mass relative to the axis of rotation.
Step 4: For a solid cylinder, the formula for the moment of inertia about its central axis is derived from integrating the mass distribution.
Step 5: The formula for the moment of inertia of a solid cylinder is I = 1/2 MR^2, where M is the mass and R is the radius of the cylinder.
Step 6: Conclude that if you know the mass and radius of the cylinder, you can use this formula to find the moment of inertia.