Fun with rotational dynamics
November 7, 2006 8:33 PM Subscribe
Recreational physics-filter: I need a solution for a tricky rotational dynamics problem.
This is a particularly challenging problem I've been playing around with. I have come up with an answer but would like to see a solution from somebody more skilled than I.
Nota bene: this isn't homework; it's just for my own edification. So you shouldn't feel bad about supplying an answer.
The problem:
Consider a bowling ball that is released with initial translational speed V(0) but which is not initially rotating. Calculate the translational speed of the ball and how far down the alley it is when it begins to roll without slipping.
No numerical values are given for any of the physical quantities involved, so the answer should be likewise.
This is a particularly challenging problem I've been playing around with. I have come up with an answer but would like to see a solution from somebody more skilled than I.
Nota bene: this isn't homework; it's just for my own edification. So you shouldn't feel bad about supplying an answer.
The problem:
Consider a bowling ball that is released with initial translational speed V(0) but which is not initially rotating. Calculate the translational speed of the ball and how far down the alley it is when it begins to roll without slipping.
No numerical values are given for any of the physical quantities involved, so the answer should be likewise.
This isn't really exotic or tricky. It's actually a fairly common worked problem in rotational dynamics. In fact, the problem and solution is laid out fairly well here (problem #3). Now if you have specific questions...
posted by vacapinta at 9:09 PM on November 7, 2006
posted by vacapinta at 9:09 PM on November 7, 2006
One thing that you should be aware of is that the formula for friction:
Force of friction = mu * Normal Force
is kind've crap. That is to say, that in most instances, if you add normal force, the friction will go up, but beyond that, it's incredibly complicated. This is especially true of transitions between slipping and sticking. The mu* Normal formula is a convenient lie that is told to give students a rough appreciation for what friction is.
So what's the real answer? No one knows. It depends on lots of other things. One example is speed (and that means both present speed and past speed ---the history matters, as well as the present). There are a variety of formulas that have been fit to experiments to produce more realistic models, but perversely, many of those fit formulas give ludicrous results in certain regimes (e.g. infinite friction when speed equals zero).
posted by Humanzee at 10:56 PM on November 7, 2006
Force of friction = mu * Normal Force
is kind've crap. That is to say, that in most instances, if you add normal force, the friction will go up, but beyond that, it's incredibly complicated. This is especially true of transitions between slipping and sticking. The mu* Normal formula is a convenient lie that is told to give students a rough appreciation for what friction is.
So what's the real answer? No one knows. It depends on lots of other things. One example is speed (and that means both present speed and past speed ---the history matters, as well as the present). There are a variety of formulas that have been fit to experiments to produce more realistic models, but perversely, many of those fit formulas give ludicrous results in certain regimes (e.g. infinite friction when speed equals zero).
posted by Humanzee at 10:56 PM on November 7, 2006
i seem to recall feynman worked this out in one of the lectures on physics, but i don't have the right volume in front of me at the moment. but you could have a look there; hard to get much more skilled than that.
posted by sergeant sandwich at 11:06 PM on November 7, 2006
posted by sergeant sandwich at 11:06 PM on November 7, 2006
You can solve for the final velocity without knowing the coefficient of friction. Consider the origin of your coordinate system to be some fixed point on the floor of the bowling alley. Then the only force acting on the bowling ball will always be pointing towards your origin, and thus the total angular momentum of the bowling ball is conserved no matter what amount of frictional force there is. At the beginning, the angular momentum of the bowling ball is solely due to its translation; once it's rolling without slipping, it has translational & rotational angular momentum, which are related in a well-defined way. From that, you should be able to solve it algebraically.
However, you need the coefficient of friction before you can solve for how far down the alley the ball goes before rolling without slipping. In the extreme case, mu = 0, it never happens, and obviously that's not the case for non-zero mu, so the answer's obviously going to depend on mu somehow.
posted by Johnny Assay at 7:54 AM on November 8, 2006
However, you need the coefficient of friction before you can solve for how far down the alley the ball goes before rolling without slipping. In the extreme case, mu = 0, it never happens, and obviously that's not the case for non-zero mu, so the answer's obviously going to depend on mu somehow.
posted by Johnny Assay at 7:54 AM on November 8, 2006
This thread is closed to new comments.
posted by hortense at 9:03 PM on November 7, 2006