Unit 10: Energy of Rotating Bodies

Practice Problems

Note: problem difficulty is ranked using a star system.

  • (*) One-star problems are fundamental to the unit, and can be done relatively quickly. Use these problems to introduce yourself to the material.

  • (**) Two-star problems are more difficult, and require an understanding of one or two key concepts. Use these problems to test your understanding of the material.

  • (***) Three-star problems are the most difficult, and require some creative thinking in addition to a deep familiarity with multiple key concepts. Use these problems to challenge yourself; if you can complete one of these, you’re on your way to mastering the material.

*Q10.1) A thin hoop of mass 10kg and radius 5cm rolls at a constant 120rpm. Calculate the following properties of the hoop (note: the moment of inertia of a thin hoop can be found using I = mr²):

a) Its rotational kinetic energy

b) Its translational kinetic energy

c) Its total kinetic energy

**Q10.2) A solid cylinder is released from rest and rolls down an incline of height 10m without slipping. Find its speed at the bottom (note: the moment of inertia of a solid cylinder can be found using I = ½mr²).

***Q10.4) A weightless string is wrapped around a pulley and connected to a 100kg block as shown below. Consider the pulley to be a solid cylinder of mass 50kg and radius 20cm. The block is released from rest and let fall 20m to the ground below. Find the angular speed of the pulley at the instant the block hits the ground (note: the moment of inertia of a solid cylinder can be found using I = ½mr²).

**Q10.3) A thin hoop of radius 20cm rolling at 240rpm encounters an inclined plane angled at 30 degrees from the horizontal. How far does the hoop travel along the surface of the inclined plane before reversing its direction of travel?