Practice: Moment of Inertia of Solids

Matthew has a model train that uses a circular cone as a flywheel. The cone has radius 𝑟 and height .

Find its moment of inertia about its axis of symmetry.

  • A2𝑚𝑟3
  • B3𝑚𝑟10
  • C2𝑚𝑟5
  • D3𝑚𝑟10
  • E𝑚𝑟

What is its radius of gyration about this axis?

  • A𝑟
  • B32𝑟
  • C310𝑟
  • D𝑟
  • E310𝑟

Matthew would like to replace the cone with a circular cylinder of the same mass. He does not want this change to affect the performance of his train, so he needs a cylinder with the same moment of inertia as the cone. Find an expression for the radius 𝑅 of the cylinder that he needs to buy.

  • A𝑅=310𝑟
  • B𝑅=310𝑟
  • C𝑅=1235𝑟
  • D𝑅=35𝑟
  • E𝑅=35𝑟

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