11.1 Rolling motion  (Page 4/6)

Conservation of mechanical energy in rolling motion

In the preceding chapter, we introduced rotational kinetic energy. Any rolling object carries rotational kinetic energy, as well as translational kinetic energy and potential energy if the system requires. Including the gravitational potential energy, the total mechanical energy of an object rolling is

In the absence of any nonconservative forces that would take energy out of the system in the form of heat, the total energy of a rolling object without slipping is conserved and is constant throughout the motion. Examples where energy is not conserved are a rolling object that is slipping, production of heat as a result of kinetic friction, and a rolling object encountering air resistance.

You may ask why a rolling object that is not slipping conserves energy, since the static friction force is nonconservative. The answer can be found by referring back to [link] . Point P in contact with the surface is at rest with respect to the surface. Therefore, its infinitesimal displacement $d\overrightarrow{r}$ with respect to the surface is zero, and the incremental work done by the static friction force is zero. We can apply energy conservation to our study of rolling motion to bring out some interesting results.

Curiosity rover

Strategy

Solution

The known quantities are $I_{\text{CM}}=m{r}^2\text{,}r=0.25\text{m,}\text{and}h=25.0\text{m}$ .

We rewrite the energy conservation equation eliminating $\omega$ by using $\omega =\frac{v_{\text{CM}}}{r}.$ We have

or

On Mars, the acceleration of gravity is $3.71{\text{m/s}}^2,$ which gives the magnitude of the velocity at the bottom of the basin as