Lecture 19: Rotating Rigid Bodies - Moment of Inertia - Parallel Axis and Perpendicular Axis Theorem - Rotational Kinetic Energy - Fly Wheels - Neutron Stars - Pulsars

author: Walter H. G. Lewin, Center for Future Civic Media, Massachusetts Institute of Technology, MIT
recorded by: Massachusetts Institute of Technology, MIT
published: Oct. 10, 2008,   recorded: October 1999,   views: 76483
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

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1. Angular Acceleration in Circular Motion:

An object in circular motion can experience a tangential acceleration (resulting in a change of its speed). Similarities between equations for linear motion and rotational motion are drawn.

2. Kinetic Energy of Rotation - Moments of Inertia:

The kinetic energy of rotation of a disk is derived and related to its moment of inertia and angular velocity. The moment of inertia depends upon the shape and mass of an object; it differs for different axes of rotation.

3. Parallel Axis and Perpendicular Axis Theorems:

The Parallel Axis theorem is very useful for calculating the moment of inertia about an axis offset from the center of mass. The Perpendicular Axis theorem is useful for thin objects.

4. Energy Management with Flywheels:

A scenario is explored where the potential energy of a car coming down a mountain is stored in a flywheel (while stepping on the brakes) rather than dissipated into heat. The rotational kinetic energy of the flywheel can, in principle, at a later time be used to increase the car's speed when needed. A demonstration shows how rotational energy in a flywheel gets converted into linear motion of a toy car.

5. Flywheels at MIT's Magnet Lab:

A pair of very massive flywheels rotating at 6 Hz are used to convert rotational kinetic energy into magnetic energy and vice versa for energy storage.

6. Rotational KE in Planets and Stars:

The rotational kinetic energy of the sun and Earth due to their spin are presented, along with data from the Crab pulsar. The Crab pulsar, with a spin period of 33 ms, is spinning down; its spin period is increasing by 36.4 nanoseconds/day. The radiated power (in the form of radio waves, light, X-rays and gamma-rays) results in a loss of rotational kinetic energy. In other words, rotational KE is converted to electromagnetic radiation.

7. Slides of MIT's Flywheel and the Crab Nebula:

Slides are shown of the Flywheels in MIT's Magnet Lab, and of the Crab Nebula (home of the Crab Pulsar). Stroboscopic pictures show that the Crab Pulsar blinks on and off in optical light as it rotates about its spin axis. An X-ray image of the Crab Nebula made with the Chandra Observatory is also shown.

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Reviews and comments:

Comment1 Shawn Chew, October 19, 2008 at 6:40 p.m.:

very clear explanation, Now i have better understanding because of all these videos. Thanks

Comment2 marco esteves, June 19, 2009 at 3:09 a.m.:

awesome!!!!!! now i can finally study astronomy at home... dispite of age and work and so and so and so!!!!
thanks guys!!! love you all!!!
no more wars.....no more guns!!!!!
lets spread knowledge so people wake up !!!!!!!!

Comment3 mariaB, December 2, 2009 at 9:19 a.m.:

This professor is excellent at lectures. He is very clear - worth every penny of tuition to register for his class, I'm sure. I will now be watching his videos to supplement my own professor's lectures.

Comment4 ahmed, December 12, 2009 at 10 p.m.:

very very awesome... i m from istanbul türkey... thank you for video...!

Comment5 Alicia Rolph, January 1, 2010 at 12:49 a.m.:

Thank you so much for explaining rotational kinetic energy.

I am using this information to better study the dead wave patterns in various states of viable and non viable consciousness. Dead Waves can amplify during sensory deprivation when triggered by certain constants. This has helped me to better understand the thresholds and parallels between the Universe and that of evolutionary data currently presented.

I believe the universe is a semi complete and identical parallel, and its patterns can be presented not only in the world but in the very research of brain function itself.

Thank you Again... I am so glad you are here for us.

Comment6 Mr.Dione, January 3, 2010 at 3:22 a.m.:

I am of brazil and i like of explication of Prof.Walter Lewin!

Comment7 c .kirty, January 6, 2010 at 9:53 p.m.:

dis guy is a genius!!!! i learnt alot from his videos.his lectures are very clear and experimentive !!! i wish we get more lectures from him!!

Comment8 a, January 11, 2010 at 8:05 p.m.:


Comment9 ishwari sharma, February 2, 2010 at 7:01 a.m.:

i have watched yr video explanation,n i m surprised that a teacher can give so clear explanation and concept of different topics of subject called physics.I m feeling so much touched with the subject n i m trying to find more n more concept.It was awesome and commendable.Thank u very much
I would have been very happy if i could have got a chance to interact n communicate with u personally.

Comment10 Srinivas acharya, May 8, 2010 at 12:25 p.m.:

01 Pl explain --- Differentiation between Moment of Inertia & Polar Moment of Inertia.

02 Pl explain --- Differentiation between Mass Moment of Inertia & Mass Polar Moment of Inertia.

Comment11 emmanuel hayford, June 10, 2010 at 3:31 p.m.:

For a series of parallel rotational axises, about which axis the body is rotating, the body has the smallest rotational inertia?

i would be glad if you could give me a solution to this problem.thank u

Comment12 T, August 25, 2010 at 9:52 p.m.:

Ahhh. Makes sense now. Need to find something a bit more advanced though, but great foundation.

Comment13 K, December 16, 2010 at 3:53 a.m.:

thanks alot, i feel like i am an MIT student now

Comment14 farid, February 17, 2011 at 6:17 p.m.:


Comment15 J Sethuraman, January 11, 2012 at 6:33 a.m.:

I am a physics teacher. I always admired Prof. Walter H. G. Lewin of MIT, his popular lecture on Rainbow is simply superb. I learn many tips to make my lecture interesting to the students.

Comment16 Daara Alfred, March 30, 2012 at 6:12 p.m.:

the handle of a wheel is 90 degree for 5 seconds. the wheel has a constant angular acceleration of 1 rad/second square. through what angle will the wheel have rotated after 10 seconds?

Comment17 Tapan Kumar Basu, India, Howrah, September 8, 2012 at 5:07 p.m.:

Lectures are Excellent. It helps in understanding Physics excellently. Prof Lewin prepared the chapters in a different meticulous approach which his viewers becomes spell bound with charm and interest. Many many sincere thanks to him. Specially now a days in developing countries there exists a dearth of Good Physics teachers.These lectures will help immensely to young and aspiring students who want to learn such a wonderful branch of Science, from a Teacher like him.

Comment18 Sagnik Das, December 7, 2012 at 5:23 p.m.:

He talks/refers to which book during his lectures anyone knows ?

Comment19 as, January 5, 2013 at 4:57 p.m.:

how can i find solution of question about this chapter.

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