What is the moment of inertia of a thin circular plate of mass M and radius R ab
Practice Questions
Q1
What is the moment of inertia of a thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?
1/2 MR^2
MR^2
1/4 MR^2
1/3 MR^2
Questions & Step-by-Step Solutions
What is the moment of inertia of a thin circular plate of mass M and radius R about an axis through its center and perpendicular to its plane?
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, it is a thin circular plate.
Step 3: Recognize the key parameters: mass (M) and radius (R) of the plate.
Step 4: Know that the formula for the moment of inertia (I) of a thin circular plate about an axis through its center is derived from integration over its area.
Step 5: The formula for the moment of inertia of a thin circular plate is I = 1/2 MR^2.
Step 6: Conclude that for a thin circular plate with mass M and radius R, the moment of inertia is I = 1/2 MR^2.
