The masses and coordinates of four particles are as follows: 40 g, x = -4.0 cm, y = 5.0 cm; 30 g, x = 5, y = 0.0 cm; 40 g, x = –5.0 cm, y = 3.0 cm; 20 g, x = 3.0 cm, y = 2.0 cm. What are the rotational inertias of this collection about the (a) x, (b) y, and (c) z axes?

Question

The masses and coordinates of four particles are as follows: 40 g, x = -4.0 cm, y = 5.0 cm; 30 g, x = 5, y = 0.0 cm; 40 g, x = –5.0 cm, y = 3.0 cm; 20 g, x = 3.0 cm, y = 2.0 cm. What are the rotational inertias of this collection about the (a) x, (b) y, and (c) z axes?

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So I used Rotational Inertia = mL^2
For x I did: (40)(-4)^2+(30)(5)^2+(40)(-5)^2+(20)(3)^2
After adding these up I have 2570 g*cm^2 which is the wrong answer. Can you please point me in the right direction? thanks!

well, you did the one for rotation about x=0, the y axis, not the x axis. The numbers are correct.

AH! Thank you!!!

Answer 1

For the x axis: (40)(5)^2+(30)(0)^2+(40)(3)^2+(20)(2)^2 = 1750 g*cm^2

For the y axis: (40)(-4)^2+(30)(5)^2+(40)(-5)^2+(20)(3)^2 = 2570 g*cm^2
For the z axis: (40)(-4)^2+(30)(0)^2+(40)(-5)^2+(20)(2)^2 = 1720 g*cm^2

Answer 2

You're welcome! I'm glad I could help. Do you have any other questions?

Answer 3

You're welcome! I'm glad I could help clarify that for you. Sometimes, it's easy to get confused when dealing with different axes of rotation. It's important to keep track of which axis you're calculating the rotational inertia for. If you have any other questions, feel free to ask!