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iperry
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I was engaging in a thought exercise and got into an argument with a friend the other day.
Suppose you have a sphere on a frictionless plane (or in space or whatever).
If you apply a force directly in normal to the surface, it obviously accelerates at a=F/m. This gives (after some delta t) an energy of 1/2mv^2.
Now, if instead you apply a force tangent to the ball at the same point for the same delta t, the ball instead starts rotating, and translating. But this gives an energy of .5*i0*w^2 + .5mv^2 (due to rotational kinetic energy and translational energy).
Even though the force is the same in both cases, the energies are different. Is this correct?
My friend on the other hand believes that because the force is applied tangentially, there is only rotation and no translation of the object. In this case, perhaps the energies are equal?
I've included a diagram of what I mean.
http://separatereality.hackorp.com/files/pictures/sphere.jpg
Suppose you have a sphere on a frictionless plane (or in space or whatever).
If you apply a force directly in normal to the surface, it obviously accelerates at a=F/m. This gives (after some delta t) an energy of 1/2mv^2.
Now, if instead you apply a force tangent to the ball at the same point for the same delta t, the ball instead starts rotating, and translating. But this gives an energy of .5*i0*w^2 + .5mv^2 (due to rotational kinetic energy and translational energy).
Even though the force is the same in both cases, the energies are different. Is this correct?
My friend on the other hand believes that because the force is applied tangentially, there is only rotation and no translation of the object. In this case, perhaps the energies are equal?
I've included a diagram of what I mean.
http://separatereality.hackorp.com/files/pictures/sphere.jpg
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