Analytical mechanics for students of physics and engineering . Fio. 74.* In general if y is a function of x then the average value of y between the 1 /•*! limits j-i and Jj is given by the relation: y = I ydx. Xi — X[ Ji. CENTER OF .MASS AND MOMENT OF [NERTIA L43 determine x only. Taking a snip of width dx for the element of m have dm = a 2 y dx = 2aV2 pxdx, where a- is the mass per unit area. Therefore substituting this expressionof dm in equation (I) and changing the limits of integration we obtain Xo . x \ 2 px dxx= -— 2a faV~2pxdx j x? dx 5 2. Find the center of mass of the lamina bounded
Analytical mechanics for students of physics and engineering . Fio. 74.* In general if y is a function of x then the average value of y between the 1 /•*! limits j-i and Jj is given by the relation: y = I ydx. Xi — X[ Ji. CENTER OF .MASS AND MOMENT OF [NERTIA L43 determine x only. Taking a snip of width dx for the element of m have dm = a 2 y dx = 2aV2 pxdx, where a- is the mass per unit area. Therefore substituting this expressionof dm in equation (I) and changing the limits of integration we obtain Xo . x \ 2 px dxx= -— 2a faV~2pxdx j x? dx 5 2. Find the center of mass of the lamina bounded by the curvesy1 = 4 ox and y = bx, Fig. 75. Let dx dij be the area of the element of mass, then dm = udxdy. Therefore substituting in equation (I) and introducing the proper limitsof integration we obtain 4a • ? X,xdJdx - X l,11* X = —T^ y = —*a 0 L dlJdX X Xr ** f bl (2 V^r - fa) X dx J; (^ OX - | X»J </x = To ££ f (2 V^ - bx) dx fbi(2Va~c- bx) dx Jo Jo 8a 562 b 144 ANALYTICAL MECHANICS 3. Find the center of mass of a semicircular lamina
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Keywords: ., bookcentury1900, bookdecade1910, bookpublishernewyo, bookyear1913
