Problem #0004 Mechanics Sub-menu Problem #0006 Chapters Chapters

5.

Problem 11.50E (HRW)

Two particles, each with mass m, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length l and mass M as shown in the figure. The combination rotates around the rotation axis with angular velocity . Obtain algebraic expressions for (a) the rotational inertia of the combination about O and (b) the kinetic energy of rotation about O.

Solution:             Click For PDF Version

(a)

As mass of each rod is m and their combined length is 2l, the moment of inertia of the rods with respect to rotation axis at O is .

The moment of inertia of the two balls about O is .

Therefore, the algebraic expression for the rotational inertia of the combination about O is

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(b)

And, the kinetic energy of rotation about O is

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