What is the moment of inertia of a thin wire bent in the shape of a semicircle o
Practice Questions
Q1
What is the moment of inertia of a thin wire bent in the shape of a semicircle of radius R and mass M about the diameter?
1/2 MR^2
1/4 MR^2
MR^2
3/8 MR^2
Questions & Step-by-Step Solutions
What is the moment of inertia of a thin wire bent in the shape of a semicircle of radius R and mass M about the diameter?
Step 1: Understand the concept of moment of inertia. 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 thin wire bent into a semicircle.
Step 3: Recognize the axis of rotation. We are calculating the moment of inertia about the diameter of the semicircle.
Step 4: Use the formula for the moment of inertia of a thin wire. For a semicircular wire, the moment of inertia about the diameter is derived from integration.
Step 5: The formula for the moment of inertia of a semicircular wire about its diameter is I = (1/2) * M * R^2, but we need to adjust it for the semicircle shape.
Step 6: After performing the necessary calculations, we find that the moment of inertia of the semicircular wire about the diameter is I = (3/8) * M * R^2.
Step 7: Conclude that the final answer is I = (3/8) * M * R^2.
