The total moment of inertia for four rods forming a square, when hung from a corner, is calculated using the Parallel Axis Theorem. The moment of inertia for one rod about its center is given by I = (1/12)ML². To find the total moment of inertia, first calculate the moment of inertia for each rod at its center, then apply the Parallel Axis Theorem to determine the new moment of inertia at the corner. The final result is 10ML²/3, taking into account the distances from the center of the square to each rod's center.
PREREQUISITESStudents studying physics, particularly those focusing on mechanics, engineers working with structural designs, and anyone interested in understanding rotational dynamics and moment of inertia calculations.
makyol said:Does it make sense firstly finding all of four rods moment of inertia at its centre then taking it and finding the new moment of inertia secondly at the corner of square?
Actually i cannot understand precisely, can you please be more clear?
rock.freak667 said:Sorry, I didn't see the hanging from the corner part.
I=(1/12)ML2.
You need to find the distances of the centres of each rod to the corner and then use the parallel axis theorem. Then just simply add them up.
Md^2 = M(5/4)L^2makyol said:Again what distance i will use?
L or squareroot of M(5/4)L^2 ?
This approach would work. The moment of inertia about the center of the square would work out to be 4/3 ML^2. Then you can apply the parallel-axis theorem to the square as a whole. You just have to be a little careful with this step because the mass of the square is 4M, not just M.makyol said:Does it make sense firstly finding all of four rods moment of inertia at its centre then taking it and finding the new moment of inertia secondly at the corner of square?