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L-Shaped object consisting of two rods, each of length l and mass m, about an axis passing through the end-point of one of the rods and perpendicular to the plane of the L Calculate the moment of inertia

L-Shaped object consisting of two rods, each of length l and mass m, about an axis passing through the end-point of one of the rods and perpendicular to the plane of the L


Calculate the moment of inertia

Grade:11

3 Answers

Swapnil Saxena
102 Points
10 years ago

Hi Siddhant,

Lets first calculate the moment of inertia of the system about an axis passing through the common-point of one of the rods and perpendicular to the plane of the L

Then the moment of inertia = 2*(ML2/3) (where ML2/3 is the moment of inertia of one rod about an axis passing about one of its endpoints)

Using Parallel Axis Theorm

Moment of Inertia of the sytem about an axis passing through the end-point of one of the rods and perpendicular to the plane of the L 

= I + Md2 (where d is the distance of the initail and final axis of rotation)

Here D= L (length of the rod)

then Moment of Inertia = 2(ML2)/3 + ((2M)L2) = 8(ML2)/3

Swapnil Saxena
102 Points
10 years ago

Sorry for the calculation mistake, The moment of inertia = (2/3) ML2 + (ML2) = 5ML2/3

ankit singh
askIITians Faculty 614 Points
2 years ago
 

calculate the moment of inertia of the system about an axis passing through the common-point of one of the rods and perpendicular to the plane of the L

Then the moment of inertia = 2*(ML2/3) (where ML2/3 is the moment of inertia of one rod about an axis passing about one of its endpoints)

Using Parallel Axis Theorm

Moment of Inertia of the sytem about an axis passing through the end-point of one of the rods and perpendicular to the plane of the L 

= I + Md2 (where d is the distance of the initail and final axis of rotation)

Here D= L (length of the rod)

 

 
 
The moment of inertia = (2/3) ML2 + (ML2) = 5ML2/3

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