Peoples Physics Concepts

http://www.ck12.org Chapter 9. Rotational Motion

9.7 Rolling Energy Problems

• Use energy conservation in situations that include rotating objects.

Students will learn how to use energy conservation in situations that include rotating objects. Remember,

conservation of energy still holds. A rolling object has two parts to its kinetic energy: the linear kinetic energy that

you’ve already done, and this rotational kinetic energy. The method to calculate the rotational energy from the

moment of inertia and rotational velocity is shown below.

Key Equations

∑Einitial=∑E

final The total energy does not change in closed systems

KErot=^12 Iω^2

Guidance

You can use energy conservation in rotation problems just like you did in the energy conservation lessons for linear

motion. Note that rotating objects also have kinetic energy of rotation and this must be included when accounting

for energy conservation.

Example 1

A hoop of mass 1 kg and radius .75 m, begins at rest at the top of a ramp, 3m above the ground. What is it’s

rotational velocity at the bottom of the ramp if the hoop rolls down the ramp without slipping?

Solution

To solve this problem, we’ll apply energy conservation to the hoop. The hoop only has gravitational potential

energy at the top of the ramp, and it has both rotational and linear kinetic energy at the bottom of the ramp.