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I have asked this question wrt this question. So I want to ask the static friction opposing not the motion of the field just helps the field to get the energy back so the work now why does not the rotational the friction oppose the oppose the motion and why does not It create heat are wasting the form of energy as friction is non conservative force it should waste some energy but the rolling friction does not when can we conclude that rolling friction is a conservative force or it is the only force that get the disk the desired speed.

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    $\begingroup$ Think of a block in a slanted plane held still by friction. It is static friction, does it waste energy? No. Only dynamic friction "wastes" (dissipate) energy $\endgroup$ – Wolphram jonny Jan 6 at 16:04
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I wouldn't call it rolling friction as that is a term usually meant to refer to lossy (heat generating) effects around bearings and axles or when there is deformation in the materials.

I believe your question refers to static friction which allows wheels to rotate instead of slide over flat surfaces and whether there is energy loss associated with it. The answer is no.

As the wheel begins to rotate, some linear kinetic energy of the wheel is converted to rotational kinetic energy as a result of static friction with zero energy dissipation in the process. This is because while static friction acts tangentially to the point of wheel/surface contact, the resulting acceleration acts perpendicularly (toward the center of the wheel). Since static friction force and rotational acceleration vectors are orthogonal, no work is done.

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  • $\begingroup$ But what if there was rolling friction then there should be a waste of energy. $\endgroup$ – Nobody recognizeable Jan 6 at 18:27
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There seems to be something wrong with the wording in the question, but if you ask why there is no heat in your original problem, while there is in reality: An object that rolls, such as a tire, gets compressed when at its lowest point, and decompressed afterwards. That movement is not accounted for in your original problem, and would create heat.

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