What is the moment of inertia of a solid cylinder of mass M and radius R about its central axis?
Correct Answer: I = 1/2 MR^2
- 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.
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