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Worksheet: Rotational Kinetic Energy

Q1:

A neutron star of mass 2 . 0 0 × 1 0 3 0 kg and radius 10.0 km rotates with a period of 0.02000 seconds. What is its rotational kinetic energy?

  • A 3 . 6 0 × 1 0 4 2 J
  • B 3 . 2 9 × 1 0 4 2 J
  • C 4 . 2 0 × 1 0 4 2 J
  • D 3 . 9 5 × 1 0 4 2 J
  • E 4 . 8 1 × 1 0 4 2 J

Q2:

A system consists of an annular cylinder of mass 1.0 kg with inner radius 20 cm and outer radius 30 cm mounted on a disk of mass 2.0 kg and radius 50 cm. The system rotates about an axis through the centers of the annular cylinder and of the disk at 10 rev/s.

What is the moment of inertia of the system?

What is the system’s rotational kinetic energy?

Q3:

A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 20.0 m/s at a distance of 0.480 m from the joint and the moment of inertia of the forearm is 0.500 kg⋅m2, what is the rotational kinetic energy of the forearm?

Q4:

A small helicopter is propelled horizontally at a speed of 20.0 m/s by the rotation at 300 rpm of four rotor blades. Each blade is 50.0 kg in mass, 4.00 m in length, and can be modeled as a thin rod that is joined at one end to an axis of rotation that is perpendicular to its length. The mass of the helicopter including its rotor blades is 1 0 0 0 kg.

Find the rotational kinetic energy of the blades.

  • A 2 . 6 3 × 1 0 5 J
  • B 1 . 3 2 × 1 0 5 J
  • C 2 . 0 0 × 1 0 5 J
  • D 5 . 2 6 × 1 0 5 J
  • E 3 . 3 6 × 1 0 5 J

Find the ratio of the rotational kinetic energy of the blades to the translational kinetic energy of the helicopter.

Q5:

A horizontal rod of length 0.500 m and negligible mass has six small washers hung from it, evenly spaced at 𝑑 = 1 0 . 0 c m apart, with a washer at each end of the rod, as shown in the diagram. Each washer has a mass of 20.0 g. The rod rotates uniformly at 5.00 rev/s about an axis at the midpoint of its horizontal length.