2007-11-09 Masses Distributed over a Plane Region

2007-11-09 Masses Distributed over a Plane Region - U y (~...

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y Each mass mk has a moment about each axis. )' A two-dimensional array of masses balances on its center of mass. .. ; .... ". (~ U "~~ ''"-'" Masses Distributed over a Plane Region Suppose we have a finite collection of masses located in the plane, with mass lIIi nt the point (x", y,,) . The mass of the system is System mass: A1 = L m". Each mass "''' has a moment about each axis. Its moment about the x-axis is and its moment about the y-axis is ",''x,,. The moments of the entire system about the two axes are . , \ Moment about x-axis: M.f = L "''')''' , M). = L III"X". Moment about )'-axis: The x-coordinate of the system's center of mass is defined to be _ My L 11I".\',,* x= A1 = 'Llllk . With this choice of x, as in the one-dimensional case, thc system balances about the line x = x. The y-coordinate of the system's center of mass is derincd to be - _ Mx _ L "'k)''' y--- . M Llllk With this choice of )', the system balances about the line y = )' as well. The torques exerted by .the masses about the line )'
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2007-11-09 Masses Distributed over a Plane Region - U y (~...

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