Angular Momentum and Energy
I teach high school physics. The ring and disk (equal
mass and radius) "racing" down the ramp demonstration is a favorite one
of my because it is hard for the students to predict but one that is
easily understood once I explain it. My question is this: While it is
true that the disk will make it down the ramp first, if we allow them
both to continue rolling along a flat surface (carpet), which will come
to rest first? I think they will both travel the same distance because
they each start with the same amount of potential energy. Am I right or
am I missing something? I've tried it buy the ring and/or disk never
goes straight until stopping. Thanks!
I would not know which one would go faster down the ramp either!!! The
problem with rolling either object on a carpet is that they will be subject
to more or less random side forces due to the texture of the carpet. And of
course once the disc or sphere gets a slight sideways direction the
trajectory is going to become random. You might try a smooth surface, or if
they go too far to be practical, use a sheet of self adhesive wall paper or
shelf paper and the tackiness of the adhesive will shorten the path of both.
In fact, this "rolling ball" or "rolling cylinder" method is used in reverse
to get some idea of the tackiness of adhesives. The ball//cylinder rolls
down a ramp at a certain angle, and then across a horizontal length of the
adhesive. The higher the "tack" of the adhesive the shorter distance the
ball/cylinder will roll. And you record the number of cm.
Absent friction, they would both roll forever on a flat surface, so the
question is "does friction care how momentum is divvied up between
linear and angular?" I suppose it does, in some complicated way that
would require details about the carpet to understand, and certainly
friction with air increases with speed. On the whole, though, I would
say there is little of fundamental interest in the distances these
I would not be so quick to make a decision on this one. When slowing down,
the force is no longer constant or conservative. Air resistance depends on
speed. Once on the floor, the disk is moving faster, so the disk initially
experiences a greater air resistance force than does the ring. In most
cases, faster objects are affected more by air resistance. I would not make
a definite judgement until I tried it. If you want the objects to roll
straight, use a long metal tube and a wooden cylinder of the same length and
mass. A solid plastic cylinder may also work. If the low-density cylinder
is too light, insert metal pegs near the center. If the metal tube is too
light, add a thin layer of wax on the inside. I would recommend a length of
at least twice the diameter.
Dr. Ken Mellendorf
Illinois Central College
If the frictional force is proportional to the mass of the disk and
ring, they should travel the same distance before stopping.
This is because, as you say, they start with the same amount of
potential energy (mgh) if they have the same mass and give up that
energy while travelling a distance d where mgh = umgd. The frictional
force is umg where u is the coefficient of friction.
To a first approximation the frictional force is proportional to the
mass, but it could depend on properties of the carpet and other second
Best, Dick Plano...
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Update: June 2012