Rotation relative velocity?

kalpeshk2011

A body is rolling without slipping. Let P be topmost point at an instant and Q bottom-most point at that instant..Is it true that Q remains stationary with respect to P all the time?

What i thought was the purely mathematical thing. P will have velocity 2v to right and Q will have 0 velocity. Velcoity of Q with respect to P comes out to be -2v. BUt thinking about it, P is always at a distance of 2r from Q. So i am confused as to what should be answer?

tiny-tim

hi kalpeshk2011!
is this a translation?

if the question was originally written in english, it was quite badly written

the way i read it is that P and Q are particular points which are identified by their position at, say 2 o'clock

since at 2.05 they'll both be in completely different positions, no they're not relatively stationary (thoguh of course they do remain at the same distance from each other)

but i expect the question is meant to mean "Let P be the topmost point at every instant and Q the bottom-most point at every instant"

haruspex

I assume this is on a level surface. Yes, P will still be 2r from Q, but velocity is a vector. Instantaneously, Q will be stationary while P will move at right angles to the line joining PQ, so the distance between them won't change. A little later, P will still be moving at right angles to the line joining it to the new lowest point, Q', but tending to move away from the new position of Q. But that is counteracted by the way Q is now moving, so the distance PQ stays fixed.

kalpeshk2011

P is a point which is initially at the top. Similarly Q is initially at the bottom..YOu didnt answer my question. Is Q always stationary with respect to P?

tiny-tim

no, they'll be in completely different positions, going round each other, so they're not relatively stationary (though of course they do remain at the same distance from each other)

kalpeshk2011

ok thank you very much :)

meldraft

I don't know which course this is meant for, but keep in mind that in car tire terminology, if it's not "slipping", then it will never roll There is actually a magnitude called "slip", which has to do with the deformation of the tire. If slip=0, it will stay in place until the end of time.

tiny-tim

i know nothing about "car tire terminology", but i do know that in "physics exam question terminology," a tyre that is rolling does not slip

(the phrase "rolling without slipping" is extremely common in physics exam questions, and indeed occurred at the start of this question)

meldraft

That's why I mentioned it, in case that it's not the typical physics course

harrylin

Yes but also no: it depends on the reference system that you assume - and in this case, you did not specify it. A point is not a reference system.

1. Q remains stationary relative to P all the time in the sense that their distance doesn't change; thus, Q and P are stationary with respect to a co-moving rotating reference system. Another, well known example is that of "geostationary" satellites.

2. Q is not stationary relative to P in the sense that Q is moving relative to P with respect to any inertial reference system - which is what we commonly use for descriptions of physics.

Harald