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In the figure, two particles, each with mass m = 0.77 kg, are fastened to each o

ID: 2261674 • Letter: I

Question

In the figure, two particles, each with mass m = 0.77 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.3 cm and mass M = 1.0 kg. The combination rotates around the rotation axis with angular speed ? = 0.33 rad/s. Measured about O, what is the combination's kinetic energy?

In the figure, two particles, each with mass m = 0.77 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.3 cm and mass M = 1.0 kg. The combination rotates around the rotation axis with angular speed ? = 0.33 rad/s. Measured about O, what is the combination's kinetic energy?

Explanation / Answer

(a) the length of the rod is 2d, andits total mass is 2M, so its rotational inertia is(2M)(2d)2/3 = 8Md2/3

The particle at the middle of the rodhas a rotational inertia of md2, and the particle at theend of the rod has a rotational inertia of m(2d)2 =4md2.

The total rotational inertia istherefore

I =8Md2/3 + 5md2 =

I = 8 * 1* 0.053^2 /3 +( 5 * 0.77*0.053^2)

I = 0.0183

KE = 0.5Iw^2

KE = 0.5 * 0.0183* 0.33*0.33

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