What Is the Center of Mass for a Rod with a Sphere Attached?

AI Thread Summary
To find the center of mass of a rod with a sphere attached, consider the masses and distances involved. The rod is 24 m long and has a mass of 4 kg, while the sphere, also 4 kg, is attached at one end. The center of mass is determined by calculating the torque equilibrium between the two ends. A diagram can aid in visualizing the problem and confirming the calculations. The final center of mass will be located at a point that balances the torques from both the rod and the sphere.
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Homework Statement


If you have a rod that is pivoted at one end with a mass of 4 kg and a length of 24 m and the other end has a sphere attached to it that is 4 kg and has a radius of 1.5 m, what is the center of mass?

Homework Equations


MXcm= m1x1 + m2x2

The Attempt at a Solution


I think that the center of mass should be where the sphere attaches to the rod, but I feel like that isn't right.
 
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The centre of mass will be the middle of the total distance where the total torque is in equilibrium.

That being said, Once you figure out the torque of one end (going clockwise), you can equate it to torque at the other end (going anticlockwise, so the rod and sphere is static) and the distance can be evaluated, which will be the distance from the end to the middle.

A diagram really helps.
 

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