Understanding Dumbbell Rotation: Laws and Material Constants

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SUMMARY

The discussion centers on the dynamics of a dumbbell's rotation, specifically how the material properties of the connecting bar affect the motion of each end when torque is applied. It highlights that if the middle bar is made of a flexible material, such as rubber, the rotation at one end will not instantaneously affect the other end due to the material's properties. The conversation references the torsion spring effect and the calculation of torsion using the formula for the spring constant (L/JG), where L is the length, J is the polar moment of inertia, and G is the shear modulus.

PREREQUISITES
  • Understanding of torque and angular motion
  • Familiarity with material properties, specifically shear modulus
  • Knowledge of torsion mechanics and spring constants
  • Basic principles of rotational dynamics
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  • Research the calculation of the polar moment of inertia for various shapes
  • Study the effects of different materials on torsional rigidity
  • Explore the application of the torsion spring formula in practical scenarios
  • Learn about the dynamics of composite materials in rotational systems
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Mechanical engineers, physics students, and anyone interested in the dynamics of rotational systems and material properties affecting motion.

Antti
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I just thought about a dumbbell (for some reason) and how one end rotates if I turn the other. If it was just a "mathematical system" with two flat cylinders and a long cylinder in between, then one end would rotate in exactly the same way as the other. But if the middle bar was rubber for example, then the rotation would be delayed in the other end. Now, is there some law describing the motion \theta(t) of the other end if I know \tau(t) (torque as function of time) of the first end. That is, if I also know the length of the middle bar and what it is made of? What material constants come into play? Could I model the bar with a simple spring instead?
 
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tiny-tim said:
Hi Antti! :smile:

(nobody else has replied, so: )

Does this help … http://en.wikipedia.org/wiki/Torsion_spring? :smile:

Well no. Say I had a dumbbell made entirely of Copper and I knew the exact shape of the whole thing. Then I'm thinking there should be some torsion-spring effect, though small, in the middle bar when I apply a torque to one end. No materials are perfectly rigid. How do you calculate this from the dimensions of the object and some (which?) material constants?
 
Try http://en.wikipedia.org/wiki/Torsion_(mechanics)" , which gives the spring constant (L/JG) of a beam under torsion.
 
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