lect116_33rev_f11

lect116_33rev_f11 - Tuesday November 29 Lecture 33 The...

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Tuesday, November 29 Lecture 33 : The center of mass (Refers to Section 7.5 in your text) Students who have mastered the content of this lecture know : what the first moment wither respect to the x- axis and with respect to the y-axis is, about the center of mass of a lamina. Students who have practiced the techniques presented in this lecture will be able to: Compute the center of mass of a lamina. 33.1 Objective Given a plate of any shape, our objective is to find the coordinates of the point P on the plate where the plate balances horizontally. To attain this objective we will study simpler situations. These will eventually lead to the answer or our main question. 33.2 Simplified center of mass problems 33.2.1 Situation #1 : Balancing two masses m 1 and m 2 on a rod of negligible weight. m 1 m 2 Suppose two masses m 1 and m 2 are fixed to a rod of negligible weight on opposite sides of a fulcrum. It is a fact based on experience that this “system” will balance if the distance d 1 between the fulcrum and m 1 and the distance d 2 between the fulcrum and m 2 are such that m 1 d 1 = m 2 d 2 The point where the system balances is called the center of mass or centroid . Suppose now that this rod of negligible mass rests on the positive x -axis of the Cartesian plane, with m 1 at the x -coordinate x 1 and m 2 at x -coordinate x 2 and the center of mass is an x -coordinate between x 1 and x 2 . Then the value of which allows this system to be balanced is the one which satisfies the equation Where d 1 = – x 1 and d 2 = – x 2 . Solving for we get:
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Definitions – The expressions m 1 x
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This note was uploaded on 12/28/2011 for the course MATH 116 taught by Professor Robertandre during the Spring '11 term at Waterloo.

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lect116_33rev_f11 - Tuesday November 29 Lecture 33 The...

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