What is the moment of inertia of a uniform rectangular plate of mass M and dimensions a x b about an axis through its center and parallel to side a?
Practice Questions
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Q1
What is the moment of inertia of a uniform rectangular plate of mass M and dimensions a x b about an axis through its center and parallel to side a?
1/12 Ma^2
1/12 Mb^2
1/3 Ma^2
1/3 Mb^2
The moment of inertia of a rectangular plate about an axis through its center and parallel to side a is I = 1/3 Mb^2.
Questions & Step-by-step Solutions
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Q
Q: What is the moment of inertia of a uniform rectangular plate of mass M and dimensions a x b 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 and parallel to side a is I = 1/3 Mb^2.
Steps: 6
Step 1: Understand what moment of inertia is. 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, it is a uniform rectangular plate with mass M and dimensions a (length) and b (width).
Step 3: Determine the axis of rotation. The axis is through the center of the plate and parallel to side a.
Step 4: Recall the formula for the moment of inertia of a rectangular plate about an axis through its center and parallel to one of its sides.
Step 5: For a rectangular plate with mass M and width b, the moment of inertia about the specified axis is given by the formula I = (1/3) * M * b^2.
Step 6: Substitute the values into the formula to find the moment of inertia.
