Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Rolling AP Problem



Prof. John P. Ertel (wizard) wrote:

I'm afraid that I really don't understand the answer given below!

It seems to me that the problem is simply one of conservation of energy.

A ball that "Rolls without Slipping" has two parts to its total
kinetic energy when moving along a horizontal surface:
(1/2) m v^2 <=> translational kinetic energy
(1/2) I w^2 <=> rotational kinetic energy ("w" is omega)
Since the ball "Rolls without Slipping" there is NO ENERGY LOST TO
FRICTION because there is ZERO MOTION of the instantaneous point of
contact in the direction of the frictional force (leading to a zero work
integral).

When the ball encounters an incline and assuming it still "Rolls without
Slipping", it goes up the incline with NO LOSS TO FRICTION, transferring
ALL of both its translational and rotational kinetic energies directly

This is not a complete answer. The problem stated that the incline plane
is frictionless. Since it requires friction to exert the torque required
to change the angular velocity, the ball will spin freely once it
reaches the incline. Its angular velocity will be constant, and the gain
of potential energy will be entirely at the expense of TRANSLATIONAL
kinetic energy. Again the condition of rolling will no longer apply
(v=Rw), and the translational velocity will decrease while the angular
velocity will remain constant.
J. Epstein