spinning vrs reciprocating mass...

[JohnnyG]

The object is a sphere with a spindle through it's center in both cases.

----O----

The object is at rest and accelerates and then stops
and reverses direction.

Both oscillate. In one case back and forth and in the
second case around the spindle.

There is a small dot on the side of the sphere. A line drawn
through the dot is on a line that is perpendicular to the spindle. O.

<- ----O.---- > back and forth

@ ----O.---- @ rotate


In both cases the dot moves the same distance and during the same period of time.

Which requires more energy rotation or straight motion and is there a very simple equation that expresses this relationship?

(An equation wherein I could insert a value
representing the variables of mass and it would tell me how much force
[relative not absolute] is needed to transverse a standard distance such as 3 centimeters.)

Would this be a linear function? Twice the distance requires two times the energy?

Thanks.