A 2 kg mass and a 5 kg mass are attached to either end of a 3 m long massless ro

Question

A 2 kg mass and a 5 kg mass are attached to either end of a 3 m long massless rod.

7. 3.5 points My Notes Ask Your Teache A 2 kg mass and a 5 kg mass are attached to either end of a 3 m long massless rod. a.) Find the center of mass of the system. m, from the 2 kg mass. Find the rotational inertia (I) of the system when rotated about: b.) the end with the 2 kg mass. c.) the end with the 5 kg mass. d.) the center of the rod. e.) the center of mass of the system. (Compare this to parts b-d. Is this what you expect?) f.) Suppose a frictionless pivot is attached at the center of mass, such that the system is free to rotate about this point in the horizontal plane. A force of 6 N is exerted kg m2 kg m2 kg m2 kg m2 perpendicular to the rod, pushing directly on the 5 kg mass. Whati rad/s2

Explanation / Answer

a) Center of mass, xcm = (m1x1 + m2x2) / (m1 + m2) = [(2 * 0) + (5 * 3)] / (2 + 5) = 2.14 m

b) I = (2 * 02) + (5 * 32) = 45 kg-m2

c) I = (2 * 32) + (5 * 02) = 18 kg-m2

d) I = (2 * 1.52) + (5 * 1.52) = 15.8 kg-m2

e) I = (2 * 2.142) + [5 * (3 - 2.14)2] = 12.9 kg-m2

f) Torque, T = I

=> = T/I = [6 * (3 - 2.14)] / 12.9 = 0.4 rad/s2

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