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Lesson: Moments of Inertia of a Mass and Radius of Gyration

Worksheet • 19 Questions

Q1:

A uniform ring of radius π‘Ÿ and mass π‘š has a particle of mass π‘š attached to it. Find the moment of inertia of the composite body about an axis passing through the centre of the ring and perpendicular to the plane of the ring.

  • A 2 π‘š π‘Ÿ 2
  • B 2 π‘š π‘Ÿ 2 2
  • C π‘š π‘Ÿ 2
  • D 2 π‘š π‘Ÿ
  • E π‘š π‘Ÿ

Q2:

Matthew has a model train that uses a circular cone as a flywheel. The cone has radius π‘Ÿ and height β„Ž .

Find its moment of inertia about its axis of symmetry.

  • A 3 π‘š π‘Ÿ 1 0 
  • B π‘š π‘Ÿ 
  • C 3 π‘š β„Ž π‘Ÿ 1 0 
  • D 2 π‘š β„Ž π‘Ÿ 5 
  • E 2 π‘š π‘Ÿ 3 

What is its radius of gyration about this axis?

  • A ο„ž 3 1 0 π‘Ÿ
  • B π‘Ÿ β„Ž
  • C 3 1 0 π‘Ÿ
  • D π‘Ÿ
  • E ο„ž 3 2 π‘Ÿ β„Ž

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.

  • A 𝑅 = ο„ž 3 5 π‘Ÿ
  • B 𝑅 = 1 2 ο„ž 3 5 π‘Ÿ
  • C 𝑅 = ο„ž 3 1 0 π‘Ÿ
  • D 𝑅 = 3 5 π‘Ÿ
  • E 𝑅 = 3 1 0 π‘Ÿ

Q3:

Find the moment of inertia of a uniform solid sphere of radius π‘Ž and mass π‘š about a chord of the sphere which lies at a distance √ 2 π‘Ž 2 from the centre of the sphere.

  • A 9 π‘š π‘Ž 1 0 2
  • B π‘š π‘Ž 2 2
  • C 2 π‘š π‘Ž 5 2
  • D 1 3 π‘š π‘Ž 2 0 2
  • E 7 π‘š π‘Ž 5 2
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