# Energy loss due to friction in Rolling Motion

I understand why rolling motion does no work. My (possibly imprecise) summary of the answer is that net work done is zero. And the role of friction is to convert translational kinetic energy into rotational kinetic energy.

(I am not interested in the specifics of that conversion - though it is both conceptually and mathematically intense).

Rather, the answers everywhere seem to indicate that NO energy is lost due to friction when rolling without slipping. But would not any conversion of energy (such as translational to rotational) involve some efficiency loss? (like a light bulb only converts x% to light and rest to heat)

Are these small enough to be neglected? Or does the concept of rolling without slipping imply that energy conversion is perfect (100%)?

Note: I understand that the concept of "rolling resistance" exists. I am talking about "ideal" rolling motion as discussed in introductory physics courses.

Rather, the answers everywhere seem to indicate that NO energy is lost due to friction when rolling without slipping.

Energy can be lost in the form of rolling resistance, sometimes called rolling friction. This is not the same as the more familiar static or kinetic friction and doesn't involve slipping.

Heat is dissipated due to the inelastic deformation of the material of a rolling object, such as the rubber of a tire, when it contacts the road. The material compresses when it contacts the road and decompresses when it leaves the road during each revolution. The squeezing and un squeezing of the material generates internal friction and heat, taking energy away from the rolling object.

For more details on rolling resistance, see this article from Wikipedia: https://en.wikipedia.org/wiki/Rolling_resistance.

Hope this helps.

• Going to the microscale, origin of the rolling friction can be identified in contact mechanics (hertzian contact). One may compute elastic deformation, (a very small) part of the kinetic energy is dissipated through deformation of the media. Apr 15 at 10:14

Consider the energy of a rolling body,
$$KE(t) = KE(t_0) - Energy\ lost\ to\ friction$$ If the energy lost to friction is zero, the kinetic energy is constant. In a freely rolling body the rotational KE is constant and the translational KE is constant.
If this rolling body suddenly meets a frictionless surface it will continue to rotate at the same rate and its linear velocity will also be unchanged.
As for conversion of energy types. Drop a massive body from height h, ($$v_0=0$$). Its potential energy at time t is
$$PE(t)=PE(t_0) - mg\delta h = mg.h(t)$$ . This is converted into kinetic energy. The kinetic energy is
$$KE(t) = mg(\delta h) - losses\ to\ friction\ (drag)$$
If we ignore drag then all the potential energy is converted into kinetic energy.

Similarly, if you begin with a rotating body held above a surface and then place this body on the surface, some rotational KE will be converted to translational KE without loss, so that total energy is conserved (if rolling resistance is ignored.)