HW8 t Moments and Products of Inertia t Moments and Products of Inertia Learning

Question

HW8 t Moments and Products of Inertia t Moments and Products of Inertia Learning Goal: To be able to find the moments and products of inertia of bodies and assemblies about various axes. In the planar kinetics of a body the moment of inertia about the center of mass, is required. It Figure 1 of 1 Resources previous l 4 of 5 l next As shown, an assembly is made up of the following: a thin ring, A, of mass mA 16.0 kg and radius r 0.250 m a thin plate, B, of mass mp-27.0 kg and dimension b- 1.45 m and four rods, each with a mass of mR 7.80 kg. (Figure 1 The assembly's height is c 1.20 m

Explanation / Answer

For a thin ring A, we have

mass mA = 16 kg   and radius r = 0.25 m

For a thin plate B, we have

mass mB = 27 kg and dimension b = 1.45 m

For each rods, we have

mass mR = 7.8 kg

The assembly's height is c = 1.2 m

Now, for an assembly the moments of inertia with respect to a principal x, y and z axes.

We know that, Iz = (Iz)upper + (Iz)lower + (Iz)rods

Iz = (1/2) mA r2 + (1/2) mB c2 + 4 [(1/12) mR (c - r)2 + mR d2

Iz = (1/2) (16 kg) (0.25 m)2 + (1/2) (27 kg) (1.2 m)2 + 4 [(1/12) (7.8 kg) (0.95 m)2 + (7.8 kg) (0.725 m)2]

Iz = [(0.5 kg.m2) + (19.4 kg.m2) + (18.7 kg.m2)]

Iz = 38.6 kg.m2

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