Turning a Straight Wire into a wheel with spokes, solve for I

In summary, a stiff uniform wire of mass M_0 and length L_0 is cut, bent, and soldered to form a circular wheel with four identical spokes. The mass and length of each spoke can be expressed as fractions of the original wire. The requested information is the moment of inertia for each spoke and the circular section.
  • #1
gkinnish
2
0

Homework Statement


A stiff uniform wire of mass M_0 and length L_0 is cut, bent, and the parts soldered together so that it forms a circular wheel having four identical spokes coming out from the center. None of the wire is wasted, and you can neglect the mass of the solder.
 
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  • #2
Can you show your work?
 
  • #3
solving for the moment of inertia i came up with 4/3(M/(L/(2pi+4))^2)
 
  • #4
gkinnish said:
solving for the moment of inertia i came up with 4/3(M/(L/(2pi+4))^2)

can you show your steps... that's not what I'm getting... some things are similar... some things are different.

The mass of each spoke is [tex]\frac{1}{2\pi + 4}*M_0[/tex]

The length of each spoke is [tex]\frac{1}{2\pi + 4}*L_0[/tex]

What's the moment of inertia of each spoke?

What's the mass of the circular section? What's the moment of inertia of the circular section?
 

1. How do you turn a straight wire into a wheel with spokes?

To turn a straight wire into a wheel with spokes, you will need to bend the wire into a circular shape and then create evenly spaced spokes by making small bends in the wire at regular intervals.

2. What tools are needed to turn a straight wire into a wheel with spokes?

The tools needed to turn a straight wire into a wheel with spokes include pliers, wire cutters, and a ruler or measuring tape to ensure the spokes are evenly spaced. A hammer and an anvil may also be helpful for bending the wire into a circular shape.

3. How many spokes should a wheel have?

The number of spokes in a wheel can vary depending on the desired strength and aesthetic of the wheel. However, it is common for a wheel to have between 16-32 spokes.

4. How do you calculate the length of wire needed for the spokes?

To calculate the length of wire needed for the spokes, you will need to measure the diameter of the wheel and the desired length of each spoke. Multiply the diameter by pi (3.14) and add the desired length of the spoke to this number to determine the length of wire needed for each spoke. Multiply this number by the number of spokes to determine the total length of wire needed.

5. How can you ensure the spokes are evenly spaced?

To ensure the spokes are evenly spaced, you can use a ruler or measuring tape to mark the desired intervals on the circular wire. You can also use a spoke divider tool, which is specifically designed for evenly spacing spokes on a wheel.

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