Three long thin sticks, each of mass M and length L, are attached at their centr

Question

Three long thin sticks, each of mass M and length L, are

attached at their centres, so that the sticks are perpendicular to

each other. Find an expression for the total moment of inertia

of the system, in terms of M and L, about an axis that is

located at the end of the stick that lies along the x-axis. The

axis of rotation is parallel to the y axis, as shown in the

diagram. Carefully show all your steps and explain your

reasoning. (Check your answer: If M = 0.40 kg, and

L = 0.50 m, then I = 0.092 kg m^2.)

Three long thin sticks, each of mass M and length L, are attached at their centres, so that the sticks are perpendicular to each other. Find an expression for the total moment of inertia of the system, in terms of M and L, about an axis that is located at the end of the stick that lies along the x-axis. The axis of rotation is parallel to the y axis, as shown in the diagram. Carefully show all your steps and explain your reasoning. (Check your answer: If M = 0.40 kg, and L = 0.50 m, then I = 0.092 kg m^2.)

Explanation / Answer

Moment of inertia of stick along X-axis = (1/3) ML^2

Moment of inertia of stick along y-axis = (1/4) ML^2

Moment of inertia of stick along Z-axis = (1/12) ML^2 +(1/4) ML^2

==> total moment of inertia = (1/3+1/4+1/12+1/4) ML^2= 0.91667 ML^2

Checking the answer

--

putting th evalues

I=0.91667*0.4*(0.5)^2=0.09167 = 0.092 kg-m^2 (approx)

so it matches with answer

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