For a rectangular plate of mass M and dimensions a x b, what is the moment of inertia about an axis through its center and parallel to side a?

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Q: For a rectangular plate of mass M and dimensions a x b, what is the moment of inertia about an axis through its center and parallel to side a?

Solution: The moment of inertia of a rectangular plate about an axis through its center parallel to side a is I = 1/12 Mb^2.

Steps: 6

Step 1: Understand what moment of inertia is. It measures how difficult it is to rotate an object around an axis.
Step 2: Identify the shape of the object. In this case, it is a rectangular plate with dimensions a (length) and b (width).
Step 3: Recognize the axis of rotation. The axis is through the center of the plate and is parallel to side a.
Step 4: Recall the formula for the moment of inertia of a rectangular plate about an axis through its center parallel to one of its sides.
Step 5: The formula for the moment of inertia (I) about the specified axis is I = 1/12 * M * b^2, where M is the mass of the plate and b is the width.
Step 6: Substitute the values into the formula if needed, but the general result is I = 1/12 * M * b^2.