UMImOT TaReTutoialAssignment.aspx Construction Materia t The Expert TA | Hum Cla

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UMImOT TaReTutoialAssignment.aspx Construction Materia t The Expert TA | Hum Class I Help HW 9 - Rotation of Rigid Bodies Begin Date: 8/28/2017 10:00:00 AM -Due Date: 10/29/2017 11:59:00 PM End Date: 12272017 6:0:00 PM (8%) Problem 12: Three identical point masses of mass M are fixed at the corners of an equilateral triangle of sides I as shown. Axis A runs through a point equidistant from all three masses, perpendicular to the plane of the triangle. Axis B runs through M, and is perpendicular to the plane of the triangle. Axes C, D, and E, lie in the plane of the triangle and are as shown. Home I M e-Axis B AxisA Axis C M, 20% Part (a) Determine an expression in tenns of Mand , for the moment of inertia ofthe masses about Asia 20% Part (b) Determine an expression for the moment of inertia of the masses about Axis B in terms ofMardi 20% Part (c) Determine an expression for the moment of inertia ofthe masses about Ass C ia tear ofMat on for the moment of inertia of the masses about Axis D in terms of M and I. Acie Dis parallel to the moment ofi 20% Part (d) Determine an expression base of the triangle. for the t of inertia of the masses about Axia E in ternas of Manad Psrotual

Explanation / Answer

a)

r = distance of each mass from the center = l/sqrt(3)

IA = moment of inertia about A = (M1 + M2 + M3) r2 = 3 M(l/sqrt(3))2 = M l2

b)

IB = moment of inertia about B = M1 (0)2 + M2 l2 + M3 l2 = 2 Ml2

c)

Ic = moment of inertia about C = M2 (0)2 + M1 (l/2)2 + M3 (l/2)2 = Ml2 /2

d)

r1 = l/sqrt(3)

r2 = sqrt(3) l/6 = r3

ID = moment of inertia about D = M1 r12 + M2 r22 + M3 r32 = M((l/sqrt(3))2 + (sqrt(3) l/6)2 + (sqrt(3) l/6)2 )

ID = M(l2/3 + l2/12 + l2/12)

ID = Ml2 /2

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