1 / 7

Rotational Energy

Rotational Energy. Circular Motion. Objects in circular motion have kinetic energy. K = ½ m v 2 The velocity can be converted to angular quantities. K = ½ m ( r w ) 2 K = ½ ( m r 2 ) w 2 The term ( m r 2 ) is the moment of inertia of a particle. Integrating Mass.

leola
Download Presentation

Rotational Energy

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Rotational Energy

  2. Circular Motion • Objects in circular motion have kinetic energy. • K = ½ m v2 • The velocity can be converted to angular quantities. • K = ½ m (rw)2 • K = ½ (mr2) w2 • The term (mr2) is the moment of inertia of a particle.

  3. Integrating Mass • The kinetic energy is due to the kinetic energy of the individual pieces. • The form is similar to linear kinetic energy. • KCM = ½ mv2 • Krot = ½ Iw2

  4. How much energy is stored in the spinning earth? The earth spins about its axis. The moment of inertia for a sphere: I = 2/5 MR2 The kinetic energy for the earth: Krot = 1/5 MR2w2 With values: K = 2.56 x 1029 J Spinning Energy The energy is equivalent to 250 million times the world’s nuclear arsenal

  5. Torque and Work • A force does work on an object acting over a distance. • A torque does work on an object rotating through an angle. r Dq

  6. Conservation of Energy • The net work done by forces on an object equals the change in kinetic energy. • The net work done by torques on an object equals the change in rotational kinetic energy.

  7. As with translational motion, power is the rate of work done. The earth is slowing due to the tides. About 28 s / century 1 part in 108 The kinetic energy is changing. DK = IwDw The power dissipation is large: About 7 billion hp Rotational Power next

More Related