A uniform rod of length L and mass M is rotated about its center. What is its mo
Practice Questions
Q1
A uniform rod of length L and mass M is rotated about its center. What is its moment of inertia?
1/3 ML^2
1/12 ML^2
1/2 ML^2
ML^2
Questions & Step-by-Step Solutions
A uniform rod of length L and mass M is rotated about its center. What is its moment of inertia?
Correct Answer: I = 1/12 ML^2
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 uniform rod.
Step 3: Know the length of the rod, which is given as L, and its mass, which is given as M.
Step 4: Recognize that we are calculating the moment of inertia about the center of the rod.
Step 5: Use the formula for the moment of inertia of a uniform rod about its center, which is I = 1/12 ML^2.
Step 6: Substitute the values of M and L into the formula if needed, but the formula itself gives the answer directly.
Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a specific axis, depending on the mass distribution relative to that axis.
Uniform Rod – A uniform rod has a constant mass per unit length, which simplifies the calculation of its moment of inertia.
Axis of Rotation – The axis about which the rod is rotated (in this case, the center) is crucial for determining the moment of inertia.
