eirik@tekchips.UUCP (Eirik Fuller) (02/28/86)
Flame me if you've seen this before, or if this is in the wrong newsgroup. I hadn't seen it before I thought of it. On a bicycle with both tires the same diameter, which wheel has a larger average angular velocity? In more concrete terms, suppose you have one of those newfangled bicycle computer gizmos. On which wheel should you mount the sensor to register more mileage? Assumptions: neglect variations in tire diameter due to tire compression. Assume that neither wheel slips. Treat this purely as a geometry problem (it is not a trick question). One small hint: I thought of this as I was grinding my way up a steep hill on my fixed gear. I am willing to collect and summarize mail responses.
hopp@nbs-amrf.UUCP (Ted Hopp) (03/04/86)
> Flame me if you've seen this before, or if this is in the wrong > newsgroup. I hadn't seen it before I thought of it. > > On a bicycle with both tires the same diameter, which wheel has a > larger average angular velocity? In more concrete terms, suppose > you have one of those newfangled bicycle computer gizmos. On which > wheel should you mount the sensor to register more mileage? > > Assumptions: neglect variations in tire diameter due to tire > compression. Assume that neither wheel slips. Treat this purely as > a geometry problem (it is not a trick question). > > One small hint: I thought of this as I was grinding my way > up a steep hill on my fixed gear. > > I am willing to collect and summarize mail responses. I guess the front wheel. The back wheel cuts inside all the turns. -- Ted Hopp {seismo,umcp-cs}!nbs-amrf!hopp
steve@anasazi.UUCP (Steve Villee) (03/05/86)
> On a bicycle with both tires the same diameter, which wheel has a > larger average angular velocity? In more concrete terms, suppose > you have one of those newfangled bicycle computer gizmos. On which > wheel should you mount the sensor to register more mileage? I would say that if you do any significant amount of turning, the front wheel will have a greater average angular velocity. You could even go to the extreme of turning the front wheel perpendicular to the rest of the bicycle, and then the front wheel could go around without any angular motion on the back wheel. I can't think of any way to give the back wheel more angular motion than the front wheel, other than lifting the bicycle off the ground. --- Steve Villee (ihnp4!terak!anasazi!steve) International Anasazi, Inc. 7500 North Dreamy Draw Drive, Suite 120 Phoenix, Arizona 85020 (602) 870-3330
daver@felix.UUCP (Dave Richards) (03/07/86)
In article <620@anasazi.UUCP> steve@anasazi.UUCP (Steve Villee) writes: >> On a bicycle with both tires the same diameter, which wheel has a >> larger average angular velocity? In more concrete terms, suppose >> you have one of those newfangled bicycle computer gizmos. On which >> wheel should you mount the sensor to register more mileage? > >I would say that if you do any significant amount of turning, the front >wheel will have a greater average angular velocity. You could even go >to the extreme of turning the front wheel perpendicular to the rest of the >bicycle, and then the front wheel could go around without any angular >motion on the back wheel. I can't think of any way to give the back wheel >more angular motion than the front wheel, other than lifting the bicycle >off the ground. > >--- Steve Villee (ihnp4!terak!anasazi!steve) How about riding the bicycle backwards? The back becomes the front and vice-versa. (this takes a special hub or something, but I've seen people do it) Dave
jr@bbncc5.UUCP (John Robinson) (03/09/86)
In article <937@felix.UUCP> daver@felix.UUCP (Dave Richards) writes: >How about riding the bicycle backwards? The back becomes the front and >vice-versa. (this takes a special hub or something, but I've seen people >do it) The wheel that steers will still turn more. Thus the front wheel still goes farther even if the bike moves backwards. Again, think of the degenerate case when the back wheel stays on one spot and the front wheel turns backwards as the whole bike pivots. A non-standard bike with a fixed front wheel and steerable back wheel would have a back wheel that traveled farther ... if you could ride it without tipping over. If both wheels steered equally and simultaneously, it seems they should turn as fast. As another variant, a trick rider might well have a rear wheel that covered more angular ground by performing a long enough wheelie. /jr
king@kestrel.ARPA (Dick King) (03/11/86)
From: eirik@tekchips.UUCP (Eirik Fuller) Newsgroups: net.puzzle Date: 28 Feb 86 15:02:18 GMT Reply-To: eirik@tekchips.UUCP (Eirik Fuller) Flame me if you've seen this before, or if this is in the wrong newsgroup. I hadn't seen it before I thought of it. On a bicycle with both tires the same diameter, which wheel has a larger average angular velocity? In more concrete terms, suppose you have one of those newfangled bicycle computer gizmos. On which wheel should you mount the sensor to register more mileage? Assumptions: neglect variations in tire diameter due to tire compression. Assume that neither wheel slips. Treat this purely as a geometry problem (it is not a trick question). One small hint: I thought of this as I was grinding my way up a steep hill on my fixed gear. I am willing to collect and summarize mail responses. Sorry about the delay if this problem has been answered before -- I don't read this group too often. When the bike goes straight both wheels turn equally (neglecting the fact that the rubber is compressed just before the wheel touches down, which I think I should neglect due to assumptions:). On a turn, the front wheel has a larger turning radius and therefore goes further. Sorry about net posting -- my site can't send to UUCP (or if it can I would appreciate someone telling me how). -dick