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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