## Lecture 15: Momentum - Conservation of Momentum - Center of Mass

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: 58451
released under terms of: Creative Commons Attribution Non-Commercial Share Alike (CC-BY-NC-SA)

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# Description

1. Conservation of Momentum:

The momentum vector, internal forces, external forces and the conservation of momentum are discussed.

2. Kinetic Energy and Momentum for a 1D Collision:

Conservation of momentum is used to calculate the final velocity of a pair of masses that collide and stick together (this is called a completely inelastic collision). It is shown that kinetic energy is then always lost, but momentum is conserved.

3. Energy and Momentum for a 2D Car Collision:

The impact time is so short that the work done by the frictional force from the road exerted on the cars during the impact can be ignored. Internal frictional forces between the cars will merge the wrecks into one mass. A momentum diagram is sketched. This is a completely inelastic collision. If we compare the moment just before and just after the collision, kinetic energy is lost, but momentum is conserved.

4. Scenarios that Increase the Kinetic Energy:

When there is a bomb explosion, the momentum and kinetic energy are zero before the explosion. Thus the total momentum must remain zero, but the kinetic energy clearly increases after the explosion. Professor Lewin does some air track experiments where the released energy is from a compressed spring; kinetic energy increases but momentum is conserved.

5. Center of Mass of a System:

The definition of the center of mass is described. The center of mass behaves as if all the matter were together at that point. The center of mass of a system of objects moves with constant speed along a straight line in the absence of external forces on the system (internal forces between the objects are allowed - e.g. the objects can collide). An example is worked calculating the position vector for the center of mass for a system of three masses. An air track demonstration shows the center of mass of an oscillating system (2 objects) is moving at constant velocity. The center of mass of a tennis racket follows a parabolic trajectory while it tumbles through the air.

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1 dilip, September 7, 2009 at 4:22 a.m.:

sir,

how can i down load this lession video? for my personal understanding.

regards.

dilip

2 anonymous, October 14, 2009 at 3:04 p.m.:

dude just go to ocw.mit.edu and go to course 8.01. you'll find all teh lectures available for download there.

3 alex, October 16, 2009 at 3:25 a.m.:

for me theres a list to the right of the video with all the different formats you can download the video in. just click the link and save

4 Ibrar, December 2, 2009 at 4:42 p.m.:

there is a sentence used in this lecture that kinetic energy is destroyed.. I think energy can neither be created nor destroyes but it can be changed from one form to another.

5 Cecilia, January 17, 2011 at 5:43 a.m.:

This is the best teacher ever. Im a junior in high school and i was completely clueless about momentum and kinetic energy until this video. GREAT video.

6 shaibi, March 22, 2013 at 4:44 a.m.:

thanks MIT, I MADE A IN THIS CLASS

7 Ali khan, December 26, 2014 at 11:14 a.m.: