Systems Of Particles And Rotational Motion

Q: A thin rod of length \$4l\$ and \$4m\$ is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passes through point \$O\$ and perpendicular to the plane of paper?

Total moment of inertia\$= I_{1} + I_{2} + I_{3} + I_{4} = 2I_{1} + 2I_{2}\$\$= 2(I_{1} + I_{2}) [I_{3} + I_{1}, I_{1} = I_{4}]\$Now, \$I_{2} = I_{3} = \dfrac {MI^{2}}{3}\$Using parallel axes theorem, we have\$I = I_{CM} + Mx^{2}\$ and \$x = \sqrt {l^{2} + \dfrac {l^{2}}{4}}\$\$I_{1} = I_{4} = \dfrac {Ml^{2}}{12} + M \left [\sqrt {l^{2} + \left (\dfrac {1}{2}\right )^{2}}\right ]^{2}\$Putting all values we getMoment of inertia, \$I = 10\left (\dfrac {MI^{2}}{3}\right )\$.

Question

A thin rod of length $4 l$ and $4 m$ is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passes through point $O$ and perpendicular to the plane of paper?

Systems Of Particles And Rotational Motion

Physics 3669 Views

A thin rod of length 4l and 4m is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passes through point O and perpendicular to the plane of paper?

Physics
3669 Views

A thin rod of length $4 l$ and $4 m$ is bent at the points as shown in figure. What is the moment of inertia of the rod about the axis passes through point $O$ and perpendicular to the plane of paper?