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A thin rod of length L and mass M is rotated about an axis perpendicular to its

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Question: 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?

Options:

  1. 1/3 ML^2
  2. 1/12 ML^2
  3. 1/2 ML^2
  4. ML^2

Correct Answer: 1/3 ML^2

Solution: 

The moment of inertia of a thin rod about an end is I = 1/3 ML^2.

A thin rod of length L and mass M is rotated about an axis perpendicular to its

Practice Questions

Q1
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?
  1. 1/3 ML^2
  2. 1/12 ML^2
  3. 1/2 ML^2
  4. ML^2

Questions & Step-by-Step Solutions

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.
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