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Worksheet: Moment of Inertia


A uniform rod of mass 1.0 kg and length 2.0 m is free to rotate about one of its ends, as shown in the accompanying diagram. If the rod is released from rest at an angle of 6 0 ∘ above the horizontal, what is the speed of the tip of the rod as it passes the horizontal position?


The major and minor radii of a thin elliptical disk of uniform density are 2.00 m and 1.00 m, respectively. The disk has a mass of 1.00 kg. Determine the moment of inertia about an axis that is perpendicular with the disk’s surface and intersects the center of the disk.


How do shear stresses and normal stresses differ?

  • AShear stresses are the absolute stresses, whereas normal stresses have been divided by the total stress.
  • BThey have different units.
  • CNormal stresses act at the surfaces of materials, whereas shear stresses act within materials.
  • DShear stresses act to slide parallel planes of material apart without changing separation, whereas normal stresses act to increase or decrease the separation between parallel planes of material.
  • ENormal stresses act within materials, whereas shear stresses act at the surfaces of materials.


What is the dimension of mass moment of inertia?

  • A 𝑀 𝐿 3
  • B 𝑀 𝑇 𝐿
  • C 𝐿 4
  • D 𝑀 𝐿 2
  • E 𝑀 𝐿


A solid sphere of radius 10 cm is allowed to rotate freely about an axis. The sphere is given a sharp blow so that its center of mass starts from the position shown in the following figure with speed 15 cm/s. What is the maximum angle that the diameter makes with the vertical?

  • A 8 . 9 ∘
  • B 7 . 9 ∘
  • C 1 1 ∘
  • D 1 0 ∘
  • E 1 2 ∘


Which of the following formulas correctly expresses the relationship between the mass moment of inertia 𝐼 and the radius of gyration π‘˜ for an object of mass π‘š ?

  • A 𝐼 = π‘š π‘˜ βˆ’ 2
  • B 𝐼 = π‘š π‘˜ 0
  • C 𝐼 = π‘š π‘˜ π‘š
  • D 𝐼 = π‘š π‘˜ 2
  • E 𝐼 = π‘š π‘˜ 1


A rod and a sphere are combined to form a system. The rod’s length 𝐿 is 0.50 m and its mass is 2.0 kg. The sphere’s radius 𝑅 is 20.0 cm and its mass is 1.0 kg. The system can rotate either about the point 𝐴 , at the opposite end of the rod to the sphere, or about the point 𝐡 , where the rod and the sphere connect, as shown in the diagram.