#KY. 2 Moment of inertia and kinetic energy Four small spheres are connected by

Question

#KY. 2 Moment of inertia and kinetic energy Four small spheres are connected by rods of negligible mass and form a rigid object. Axis of rotation The figure to the right shows the situation including the axis of rotation. The spheres may be regarded as particles at the ends of the rods. In this case, n-,-,-, = a, 2 2b (a) Calculate moment of inertia of this structure. (Ans. 6ma2) 4 (b) With respect to a reference line, the angle of the rod joining 1 and 2 (or 3 and 4) is given by At, where A is a constant. Calculate the kinetic energy of the structure as a function 2a of time.

Explanation / Answer

a)

I = m1 r12 + m2 r22 + m3 r32 + m4 r42

I = m a2 + m a2 + (2m) a2 + (2m) a2

I = 6 ma2

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