A uniform lamina ABCD is in the shape of a parallelogram and its mass per unit area is u. Axes Ox, Oy are chosen, with O the point on AB such that AO = 2/3AB. Points A, B, C and D(adsbygoogle = window.adsbygoogle || []).push({});

have coordinates (-2a, O), (a, O), (2a, b) and (-a, b) respectively. Find the x and y coordinates of the centre of mass of ABCD.

(I have done this, it is (0,b/2)).

Triangles ASD and BCT (right angled triangles at each end of the parallelogram) are folded over SD (stright line from D to x-axis) and BT (straight line from B to intersection with CD) respectively so that they lie flat on the rectangular region SBTD. Find the x and y coordinates of the centre of mass of the newly formed body.

(Same answer as previous one).

This body is now pivoted freely at the point P (3a/4, b/3) and is in equilibrium with its plane vertical.

(a) Find the tangent of the angle between the line BT and the vertical.

(b) Find also the magnitude of the couple that must be applied to the body for it to rest in equilibrium with the edge DT vertical.

Help! :(

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# Centre of Mass Help

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