Rotation vs Translation for elbow joint

AI Thread Summary
The discussion clarifies the concepts of rotation and translation in the context of a beam pivoting about a hinge. When the string is cut, the beam experiences both rotation and translation, as the center of mass moves in a circular path. Although the movement may not be linear, the center of mass's motion can still be classified as translation. To achieve pure rotation without translation, adjustments to the elbow joint's position are necessary. Overall, the motion can be analyzed by decomposing it into both rotational and translational components.
physics gal
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If I were to cut the string and let the board move, I know I would get rotation. But, since the center of mass of the beam is moving as well (in a circle) could I also say that the board is translating once the string is cut?
 
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Yes.
Assuming the beam is free to pivot about the hinge at its left end, it would both rotate and translate.
 
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.Scott said:
Yes.
Assuming the beam is free to pivot about the hinge at its left end, it would both rotate and translate.
So even though the beam will be tracing a large circle around the hinge (or more likely swinging back and forth) we can call this translation? My reasoning was because the center of mass of the board is moving as it swings. Is that correct?
 
.Scott said:
Yes.
Assuming the beam is free to pivot about the hinge at its left end, it would both rotate and translate.
The Centre of Mass of the board would drop and move to the left so that would be looked upon as translation. To avoid this, you would need to (appropriately) raise the elbow joint and move it to the right. Then you would have only rotation
 
sophiecentaur said:
The Centre of Mass of the board would drop and move to the left so that would be looked upon as translation. To avoid this, you would need to (appropriately) raise the elbow joint and move it to the right. Then you would have only rotation
Even though not all movement vectors of the object are moving in space by the same amount in a given direction, we can still call this translation?
 
physics gal said:
Even though not all movement vectors of the object are moving in space by the same amount in a given direction, we can still call this translation?
Why not? The translation doesn't need to be in a straight line or in a chosen direction. We are talking in terms of translation of the CM.
 
physics gal said:
If I were to cut the string and let the board move, I know I would get rotation. But, since the center of mass of the beam is moving as well (in a circle) could I also say that the board is translating once the string is cut?
Yes, you can decompose the same motion into rotation and translation in different ways.
 
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