On 30/7/2007 9:00 AM, Michel Jullian wrote: > > ----- Original Message ----- > From: "Harry Veeder" <[EMAIL PROTECTED]> > Sent: Sunday, July 29, 2007 8:55 PM > >>>> If you could stop the Earth rotating, the wheel that has the brake on will >>>> continue to remain at rest wrt to the ground but the other wheel will >>>> continue to turn once per day wrt to the ground. >>>> >>>> The two motions differ, but the difference is masked by the rotation of the >>>> Earth. >>>> >>>> Do you agree? >>> >>> I would say on the contrary that they do not differ, unless the Earth stops >>> rotating. Releasing a brake between parts which have no tendency to move wrt >>> each other will make no difference whatsoever, agreed? >>> >>> Michel >>> >> >> No, and here is an argument without stopping the Earth's rotation. >> Mount each supporting frame on its own turntable. A slight turn of each >> turntable will show that only the wheel with the braked released is rotating >> about its own centre. > > 1/ It's about as unlikely that the Earth will be given a slight turn (by the > hand of God?) as it is that it might stop rotating, but you're right, to be > complete I should have said "they do not differ, unless the Earth's rate of > rotation changes one way or another".
I should have emphasised that the hand of god is not required in this example. The hub rests in a frame and the frame sits on a turntable and the turntable sits on the ground. If I swivel the turntable 90 (or by any amount) after the brake is released a person standing next to the wheel will be able to discover that the wheel is rotating (1 rev./day) about its hub. > The reasons have been helpfully given by > Horace and you seemed to agree with them (with unnecessary defensiveness > though if I may give an independent observer's impression) > > 2/ Actually my "agreed?" question referred to my second sentence above: > "Releasing a brake between parts which have no tendency to move wrt each other > will make no difference whatsoever" [...implied: in their relative motion, > which will remain null] > 3/ The initially braked wheel and the Earth in your scenario are in the case > of point 2 above. The rotation of the Earth "shakes" the wheel around > admittedly, but the wheel being frictionless this shaking around only produces > a radial force which as Horace pointed out produces no torque so no change in > angular momentum. > > 4/ There is no rotation of the wheel wrt its hub after the brake is released, > agreed? Unfortunately no. If I agreed then I would also find this rule of satisfactory: The angular momentum of the wheel depends only on its apparent motion. Harry
