What is the moment of inertia of a uniform thin square plate of mass M and side length a about an axis through its center and parallel to one of its sides?
Practice Questions
1 question
Q1
What is the moment of inertia of a uniform thin square plate of mass M and side length a about an axis through its center and parallel to one of its sides?
1/6 Ma²
1/12 Ma²
1/4 Ma²
1/3 Ma²
The moment of inertia of a square plate about an axis through its center and parallel to one side is I = 1/12 Ma².
Questions & Step-by-step Solutions
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Q
Q: What is the moment of inertia of a uniform thin square plate of mass M and side length a about an axis through its center and parallel to one of its sides?
Solution: The moment of inertia of a square plate about an axis through its center and parallel to one side is I = 1/12 Ma².
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 thin square plate.
Step 3: Note the mass (M) of the plate and the length of one side (a).
Step 4: Recognize that we need to find the moment of inertia about an axis that goes through the center of the plate and is parallel to one of its sides.
Step 5: Use the formula for the moment of inertia of a square plate about the specified axis, which is I = 1/12 Ma².
Step 6: Substitute the values of M and a into the formula if needed, but the formula itself gives the answer directly.
