The rigid object shown in Fig. 10-59 consists of three balls and three connectin

Question

The rigid object shown in Fig. 10-59 consists of three balls and three connecting rods, with M = 1.2 kg, L = 0.20 m, and theta = 30*. The balls may be treated as particles, and the connecting rods have negligible mass. Determine the rotational kinetic energy of the object if it has an angular speed ot 1.4 rad/s about (a) an axis that passes through point P and is perpendicular to the plane of the figure and (b) an axis that passes through point P, is perpendicular to the rod of length 2L, and Iks in the plane of the figure. Fig. 10-59

Explanation / Answer

K = 1/2 m v2 = 0.5*m*r2*w2

>>>> K = 0.5*1.2*(1.4)2 * (r12 + r22 + r32)

>>>> K = 1.176 * (r12 + r22 + r32)

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a)

>>>> K = 1.176 * ((L)2 + (L)2 + (2L)2)

           = 1.176 * ((0.2)2 + (0.2)2 + (2*0.2)2)

           = 1.176 * (0.04 + 0.04 + 0.16)

           = 0.282 Jouls

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b)

>>>> K = 1.176 * ((L*cos30)2 + (L*cos30)2 + (2L)2)

           = 1.176 * ((0.173)2 + (0.173)2 + (2*0.2)2)

           = 0.22 Jouls

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