A 3 kg mass and a 6 kg mass are attached to either end of a 3 m long massless ro

Question

A 3 kg mass and a 6 kg mass are attached to either end of a 3 m long massless rod.

a.) Find the center of mass of the system.
(2m, correct) m, from the 3 kg mass.

Find the rotational inertia (I) of the system when rotated about:
b.) the end with the 3 kg mass.
(54, correct) kg m2
c.) the end with the 6 kg mass.
(27, correct)  kg m2
d.) the center of the rod.
(I CANNOT ANSWER THIS AND NEED AN ANSWER FOR IT) kg m2

e.) the center of mass of the system.
(18  kg m2 correct)
(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 9 N is exerted perpendicular to the rod, pushing directly on the 6 kg mass. What is the size of the system's angular acceleration that would result?
(0.5 rad/s2 correct)

all of my answers were correct except d. I need to find the correct answer for d. I do not need all the other answers. ONLY D. Please help

Explanation / Answer

center of mass = m2 * L / (m1 + m2)

center of mass = 3 * 6 / (3 + 6)

center of mass = 2 m from 3 kg mass

rotational inertia = mass * radius^2

when rotated with 3 kg mass end = 6 * 3^2

when rotated with 3 kg mass end = 54 kg.m^2

when rotated with 6 kg mass end = 3 * 3^2

when rotated with 6 kg mass end = 27 kg.m^2

when rotated from the center of rod = 6 * 1.5^2 + 3 * 1.5^2

when rotated from the center of rod = 20.25 kg.m^2

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