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
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
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