A thin rod of length L and mass M is rotated about an axis perpendicular to its length and passing through one end. What is its moment of inertia?
Correct Answer: I = 1/3 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 thin rod.
- Step 3: Note the length of the rod, which is given as L, and its mass, which is given as M.
- Step 4: Recognize that the axis of rotation is at one end of the rod and is perpendicular to its length.
- Step 5: Use the formula for the moment of inertia of a thin rod rotating about an end, which is I = 1/3 ML^2.
- Step 6: Substitute the values of M and L into the formula to find the moment of inertia.
- Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis.
- Axis of Rotation – The axis about which the object is rotated significantly affects the calculation of the moment of inertia.
- Thin Rod Properties – Understanding the properties of a thin rod, including its mass distribution, is crucial for calculating its moment of inertia.
