# Rotation vs Translation for elbow joint

• I
physics gal

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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.Scott
Homework Helper
Yes.
Assuming the beam is free to pivot about the hinge at its left end, it would both rotate and translate.

sophiecentaur
physics gal
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?

sophiecentaur
Gold Member
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

physics gal
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?

sophiecentaur
Gold Member
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.

A.T.