7.5 Rotational kinetic energy: work and energy revisited  (Page 6/9)

Phet explorations: my solar system

Build your own system of heavenly bodies and watch the gravitational ballet. With this orbit simulator, you can set initial positions, velocities, and masses of 2, 3, or 4 bodies, and then see them orbit each other.

Section summary

• The rotational kinetic energy ${\text{KE}}_{\text{rot}}$ for an object with a moment of inertia $I$ and an angular velocity $\omega$ is given by
  ${\text{KE}}_{\text{rot}}=\frac{1}{2}{\mathrm{I\omega }}^2.$
• Helicopters store large amounts of rotational kinetic energy in their blades. This energy must be put into the blades before takeoff and maintained until the end of the flight. The engines do not have enough power to simultaneously provide lift and put significant rotational energy into the blades.
• Work and energy in rotational motion are completely analogous to work and energy in translational motion.
• The equation for the work-energy theorem    for rotational motion is,
  $\text{net}W=\frac{1}{2}{\mathrm{I\omega }}^2-\frac{1}{2}I{{\omega }_{\text{0}}}^2.$

Conceptual questions

The Earth has more rotational kinetic energy now than did the cloud of gas and dust from which it formed. Where did this energy come from?

Problems&Exercises