# Calc07ex - Chapter 7 Extra Topics Crater Lake Oregon Photo...

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Chapter 7 Extra Topics Crater Lake, Oregon Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 1998

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Lake Superior, Washburn, WI Photo by Vickie Kelly, 2004 Centers of Mass: Torque is a function of force and distance. (Torque is the tendency of a system to rotate about a point.) d g F
If the forces are all gravitational, then torque mgx = If the net torque is zero, then the system will balance. Since gravity is the same throughout the system, we could factor g out of the equation. O k k M m x = This is called the moment about the origin . 1 m g 2 m g

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If we divide M o by the total mass, we can find the center of mass (balance point.) O k k M m x = k k O k x m M x M m = =
For a thin rod or strip: δ = density per unit length moment about origin: ( 29 b O a M x x dx δ = ( δ is the Greek letter delta .) mass: ( 29 b a M x dx δ = k k O k x m M x M m = = center of mass: O M x M = For a rod of uniform density and thickness, the center of mass is in the middle.

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