Rotation vs Translation for elbow joint

[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?

 

[.Scott]

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

 

[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]

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]

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.]

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.