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For a thin circular ring of mass M and radius R, what is the moment of inertia a

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Question: For a thin circular ring of mass M and radius R, what is the moment of inertia about an axis perpendicular to its plane through its center?

Options:

  1. MR^2
  2. 1/2 MR^2
  3. 2/3 MR^2
  4. 1/3 MR^2

Correct Answer: MR^2

Solution: 

The moment of inertia of a thin circular ring about an axis through its center and perpendicular to its plane is I = MR^2.

For a thin circular ring of mass M and radius R, what is the moment of inertia a

Practice Questions

Q1
For a thin circular ring of mass M and radius R, what is the moment of inertia about an axis perpendicular to its plane through its center?
  1. MR^2
  2. 1/2 MR^2
  3. 2/3 MR^2
  4. 1/3 MR^2

Questions & Step-by-Step Solutions

For a thin circular ring of mass M and radius R, what is the moment of inertia about an axis perpendicular to its plane through its center?
  • 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 ring.
  • Step 3: Recognize the mass (M) and radius (R) of the ring. These are important for calculating the moment of inertia.
  • Step 4: Recall the formula for the moment of inertia of a thin circular ring about an axis through its center and perpendicular to its plane, which is I = MR^2.
  • Step 5: Substitute the values of mass (M) and radius (R) 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 changes in its rotation about an axis.
  • Thin Circular Ring – A thin circular ring is a one-dimensional object with mass distributed along its circumference, which simplifies the calculation of its moment of inertia.
  • Axis of Rotation – The axis of rotation is the line about which the object rotates; in this case, it is perpendicular to the plane of the ring and passes through its center.
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