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For a composite body made of two solid cylinders of mass M1 and M2 and radius R,

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Question: For a composite body made of two solid cylinders of mass M1 and M2 and radius R, what is the total moment of inertia about the same axis?

Options:

  1. I1 + I2
  2. I1 - I2
  3. I1 * I2
  4. I1 / I2

Correct Answer: I1 + I2

Solution: 

The total moment of inertia of a composite body is the sum of the individual moments of inertia: I_total = I1 + I2.

For a composite body made of two solid cylinders of mass M1 and M2 and radius R,

Practice Questions

Q1
For a composite body made of two solid cylinders of mass M1 and M2 and radius R, what is the total moment of inertia about the same axis?
  1. I1 + I2
  2. I1 - I2
  3. I1 * I2
  4. I1 / I2

Questions & Step-by-Step Solutions

For a composite body made of two solid cylinders of mass M1 and M2 and radius R, what is the total moment of inertia about the same axis?
  • Step 1: Identify the two solid cylinders. Let's call them Cylinder 1 with mass M1 and Cylinder 2 with mass M2.
  • Step 2: Understand that the moment of inertia (I) for a solid cylinder about its central axis is given by the formula I = (1/2) * M * R^2, where M is the mass and R is the radius.
  • Step 3: Calculate the moment of inertia for Cylinder 1 using its mass M1: I1 = (1/2) * M1 * R^2.
  • Step 4: Calculate the moment of inertia for Cylinder 2 using its mass M2: I2 = (1/2) * M2 * R^2.
  • Step 5: Add the two moments of inertia together to find the total moment of inertia: I_total = I1 + I2.
  • Step 6: Substitute the values from Step 3 and Step 4 into the equation: I_total = (1/2) * M1 * R^2 + (1/2) * M2 * R^2.
  • Step 7: Factor out the common terms: I_total = (1/2) * (M1 + M2) * R^2.
  • Moment of Inertia – The moment of inertia is a measure of an object's resistance to rotational motion about a given axis, calculated as the sum of the products of mass and the square of the distance from the axis of rotation.
  • Composite Bodies – A composite body is made up of two or more individual bodies, and the total moment of inertia is found by summing the moments of inertia of each individual body.
  • Parallel Axis Theorem – If the axis of rotation is not through the center of mass, the parallel axis theorem may need to be applied to find the correct moment of inertia.
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