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Three identical uniform rods each of length 40cm and mass 2kg form an equilateral triangle. Find the moment of inertia of this system about an axis passing through one corner ? Thanks in advance !

Three identical uniform rods each of length 40cm and mass 2kg form an equilateral triangle. Find the moment of inertia of this system about an axis passing through one corner ?


 


Thanks in advance !

Grade:12

2 Answers

vikas askiitian expert
509 Points
10 years ago

let ABC is the triangle formed by these rods then we have to find moment of inertia any about vertex , let vertex be A...

then , rod AB & AC will have same moment of inertia about end A ,

IAC = IAB = mL2/12 + mL2/4 = mL2/3

moment of inertia of BC  = mL2/12 + md2                     (d is perpendicular distance from axis of rotation)

      from triangle ABC , d = Lcos30

         IBC = mL2/12 + 3mL2/4 = 10mL2/12

net moment of inertia = IAB+IBC+IAC

                     Inet   =18mL2/12 = 3mL2 /2

                    Inet = 0.48kg-m2

approve my ans if u like it

Sudheesh Singanamalla
114 Points
10 years ago

Thanks a Lot

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