Relativity

[Khandro]

Thoughts on my early morning walk along the river with my dog :

If a bicycle & rider are travelling in a northerly direction at 10mph. at any given moment, the top of the front wheel is travelling past the fork, so it must be travelling (in relation to the fork & ground) at 10mph plus. Meanwhile at the same moment, the bottom of the wheel is travelling in a southerly direction so it can't be moving at the same speed as fork, so it should be travelling at 10mph minus
Are the top & bottom of the wheel travelling in two directions and at different speeds? What's going on here?
Or should I have stayed in bed? :0)

[dannyk13]

Stayed in bed.

[johnk]

They are traveling relative to the ground in different directions at different speeds with the point of the wheel on the ground not moving at all and then accelerates as it leaves the ground to maximum speed at the top. Relative to the ground any point on the wheel is reciprocating from maximum speed forwards to maximum speed backwards. I think I'll go to bed!!

[bhg481]

The linear velocities are different but the angular velocities of all the points on the wheel are the same.

[davebro]

https://www.animations.physics.unsw.edu.au/jw/rolling.htm

[jim360]

This would be true in relation to the fork, but not the ground. Indeed, it's necessary for the top and bottom of the wheel to be moving equally and oppositely relative to the fork/axle, otherwise the wheel would quickly lose its shape (or fall off the axle, or some such). Relative to the ground, no part of the wheel would be moving backwards at any point in the motion.

The overall forward motion relative to the ground is being generated, at least partly, because of contact with the ground that's generating friction. Indeed, since the wheel is "trying" to spin backwards against the ground, the frictional force points *forwards*.

[jim360]

NB as shown in davebro's link above, parts of a train's wheel *do* move backwards briefly, but that's because those parts are *below* the point of contact between wheel and rail. Anything above the point of contact is always moving forwards, and at the point of contact itself the wheel is very briefly stationary (because its velocity due to the wheel spinning is equal and opposite to the forwards motion of the bicycle).

[1ozzy]

I nearly understood that Jim, hmm, must keep thinking

[Khandro]

jim, Thank you, so to the observer, the whole wheel is moving at 10mph northwards, but to the rider, the bottom of the wheel is moving southwards and must then be travelling slower the the top ? then the only part of the wheel moving at 10mph would be the front and back horizontal to the axle ? but they are not constant, so every part of the wheel is moving at different speeds while also, depending on your point of view, moving at 10mph. ?

[Khandro]

and in different directions

[TheChair]

They are travelling at different speeds relative to the ground, but they are both travelling in the same direction. Each one will trace a sine wave forwards, 180 degrees out of phase with the other.

[dannyk13]

All that needs to be known is that the wheel rotates and propels the cycle forwards.QED

[jno]

if one spot on the outer surface of your wheel is moving at a different speed from another spot on the outer surface of your wheel, then your wheel is falling apart and you should hop off.

[Khandro]

TheChair

//They are travelling at different speeds relative to the ground, but they are both travelling in the same direction. Each one will trace a sine wave forwards, 180 degrees out of phase with the other.//

In my example, only the top of the wheel is travelling northwards, the bottom of the wheel is travelling southwards (but also northwards) to both the observer and the rider, that is the paradox, it would seem.

[THECORBYLOON]

Why is it a paradox? Opposite ends of a see-saw travel in opposite directions at the same speed if the pivot is in the middle but that's not a paradox.

[ToraToraTora]

your OP is flawed, if you traced a point on the wheel you'd see that no part of the wheel is going backwards. However you are correct with the bottom of a railway wheel flange overhanging the rail, if you traced that you'd see a small loop where the bottom does indeed go backwards a small amount.

[davebro]

The wheel never goes backwards relative to the ground. The bottom of the wheel is in contact with the ground, the ground is stationary so that point of the wheel is stationary. It then accelerates to max speed at the top. The curve followed by a point on the wheel is a cycloid (see article) not a sine wave.

jno - we are talking speeds relative to the ground. The rim of the wheel has the same rotational velocity all around.

[Khandro]

TTT //your OP is flawed, if you traced a point on the wheel you'd see that no part of the wheel is going backwards//

I haven't said it is moving 'backwards' (in relation to the ground) I have said it is moving in a southerly direction, while overall, moving northwards. that seems to me to be beyond dispute.

Though the circumstances are different, think of a train moving north & a man walking down the corridor towards the end of the train - he is walking in a southerly direction, though also moving northwards.

[Peter Pedant]

hi Jim

[ABerrant]

Perhaps a better example is the helicopter, where the relative difference in speeds of the advancing and retreating rotor blades effectively limit the maximum speed of the aircraft through blade stall or asymmetric transonic drag.

https://en.wikipedia.org/wiki/Slowed_rotor#Speed_limits_of_aircraft_rotors

[jno]

davebro, just responding to the post at 09:15 every part of the wheel is moving at different speeds