Question: If a solid cylinder is rotated about its diameter, what is its moment of inertia?
Options:
1/2 MR^2
1/4 MR^2
1/3 MR^2
MR^2
Correct Answer: 1/4 MR^2
Solution:
The moment of inertia of a solid cylinder about its diameter is I = 1/4 MR^2.
If a solid cylinder is rotated about its diameter, what is its moment of inertia
Practice Questions
Q1
If a solid cylinder is rotated about its diameter, what is its moment of inertia?
1/2 MR^2
1/4 MR^2
1/3 MR^2
MR^2
Questions & Step-by-Step Solutions
If a solid cylinder is rotated about its diameter, what is its moment of inertia?
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, we have a solid cylinder.
Step 3: Recognize that we are rotating the cylinder about its diameter.
Step 4: Recall the formula for the moment of inertia of a solid cylinder about its diameter, which is I = 1/4 MR^2.
Step 5: In the formula, 'M' represents the mass of the cylinder and 'R' represents the radius of the cylinder.
Step 6: Substitute the values of mass and radius into the formula if needed, but the general formula is I = 1/4 MR^2.
Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a specific axis.
Solid Cylinder Properties – Understanding the geometric and mass distribution properties of a solid cylinder is crucial for calculating its moment of inertia.
Axis of Rotation – The axis about which the object is rotated significantly affects the moment of inertia value.
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