A rotating system is composed of a long rod with a length of 3.4·m (L1) and a ma

Question

A rotating system is composed of a long rod with a length of 3.4·m (L1) and a mass of 2.4·kg . Attached to each end is a solid disk and smaller rod perpendicular to the first. The solid disk has a mass of 0.5·kg and radius of 0.25·m. The smaller rod has a length of 0.4·m (L2) and mass of 2.3·kg.

(a) What is moment of inertia of the long bar?2.312  Kg m2
(b) What is the rotational of inertia of the rotating disk?1.917  Kg m2
(c) What is the rotational of inertial of the smaller bar? 6.678  Kg m2
(d) What is the rotational inertial of the system?

Explanation / Answer

(A) I1 = m1 L1^2 / 12

= 2.4 x 3.4^2 / 12

= 2.312 kg m^2

(b) about its C.m. = m r^2 / 2

I2 = m r^2 /2 + m d^2

= (0.5 x 0.25^2 / 2) + (0.5)(0.25 + (3.4/2))^2

= 1.917 kg m^2

(C) I3 = (2.3 x 0.4^2 / 12) + (2.3)(3.4/2)^2

I3 = 6.678 kg m^2

(D) I = I1 + I2 + I3 = 10.9 kg m^2

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