1. Center of Mass
Section 7.8

2. • Why do we need to calculate the center of mass?
• How do we calculate the center of mass?
Center of Mass

3. • For all of our motion problems we have treated every
object like a point mass
• We have also said that the only motion has been
translational (*)
• Is this legit?
Center of Mass

4. • Part A, the motion is
purely translational
• Part A has translation
and rotation
• Note that one point
moves in a
parabola, which is
how we treated it
Diver

5. Tossing a wrench

6. • http://www.youtube.com/watch?v=DY3LYQv22qY
Demo

7. • General Motion of an object =
• Sum of translational motion of the CM
• Plus rotational, vibrational, etc.. Motion about the CM
Center of Mass

8. •
Calculating CM

9. • Center of gravity: the point
where the gravitational
force can be considered to
act
• If you hung something at
any point other than the
center of gravity, it would
pivot
• Usually the same as the
center of mass
Center of Gravity

10. • Found experimentally
by suspending objects
• Can be out side the
object
• Doughnut’s is in the
center of the hole
Center of Mass

11. • Three people of roughly the same equal mass
m on a lightweight air filled banana boat sit
along the x axis of positions xA = 1.0 m, xB =
5.0 m and xC = 6.0 m, measured from the left
hand position.
• Find the position of the CM. Ignore the mass
of the boat
Example

12. • Read Section 7.7
• Do Problems # 46 - 50, Page 189
Homework