what is the difference between pure translational motion and translation motion?

"Pure translational" motion means the object is moving from place to place but isn't rotating at all. Mathematically, that means every point on the object has the same velocity vector as every other point on the object. For example, say you have a box that's sliding along the ground, and say each corner on the box is moving at 15 feet per second at an angle of 26 degrees west of north. Since every point on the box has the same velocity vector, the motion is "pure translational." 

Translational motion (also called linear) is simply an increment of distance dS travelled over an increment of time dT. As dS is a straight line over this small increment, there is no angular momentum. That is, there is no rotation or revolution of the object with the linear motion

"Pure rotational" motion means the object is rotating, but its position in space isn't changing. Mathematically, that means that every point on the object moves in a circle around some axis (usually through the object's center of mass).

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