Center of MassSection 7.8

Center of Mass

• Why do we need to calculate the center of mass?

• How do we calculate the center of mass?

Center of Mass

• 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?

Diver

• 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

Tossing a wrench

Demo

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

Center of Mass

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

Calculating CM

• For two particles

• M is total mass

• Note where you are measuring from

Center of Gravity

• 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 Mass

• Found experimentally by suspending objects

• Can be out side the object

• Doughnut’s is in the center of the hole

Example

• 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

Homework

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