10_1425_web_Lec_17_CenterOfMassEtc

10_1425_web_Lec_17_CenterOfMassEtc - Center of Mass Physics...

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Center of Mass Physics 1425 Lecture 17 Michael Fowler, UVa
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Center of Mass and Center of Gravity Everyone knows that if one kid has twice the weight, the other kid must sit twice as far from the axle to balance. Each kid then has the same torque about the axle: Torque = force x distance from the axle of the force’s line of action. The gravitational forces balance about the axle: it’s at the center of gravity—aka the center of mass. Kids on seesaw x 2 mg CM 2 x mg
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Center of Mass in One Dimension Recall the center of mass of two objects is defined by Notice that if we take x CM as the origin (the center of mass frame ) then the equation is just precisely the balance equation from before (one of those x ’s is negative, of course). ( ) 1 2 CM CM 1 1 2 2 m m x Mx m x m x += = + 11 2 2 0 mx mx
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CM of Several Objects in One Dimension The general formula is: But before putting in numbers, it’s worth staring at the system to see if it’s symmetric about any point!
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10_1425_web_Lec_17_CenterOfMassEtc - Center of Mass Physics...

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