Wheel paradox

[OldJohnnyYen]

This is frying my brain, I can't think of a single way of explaining this properly.

http://io9.com/the-wheel-paradox-that-stumped-aris...

[motorizer]

the smaller circle is moving further in a linear fashion than it would need to in order to "unroll" so it would be sliding, if you get what I mean.

[OldJohnnyYen]

I don't sorry, the only way I can understand it is by coming to the concluding that the smaller wheel just doesn't exhist, it's part of the larger wheel.

[Simpo Two]

The small wheel is being carried along sideways by the larer wheel, so there are two motions in action = the whole.

[CubanPete]

It's not that hard chaps.

[Brother D]

Think of the extreme case

What is the center of the hub doing? - its moving linearly in a straight line.

[tvrolet]

The smaller wheel must skid along the path. It cannot be 'in contact' - it both other and inner wheels were locked on to their respective surfaces/paths then the whole wheel would be 'locked'.

Think of it as a gear-pair out a gearbox with with 3 difference sizes of gear. You could not engage them simultaneously onto another gear. Or imaging that it's the smaller wheel on a table or similar controlling the speed. If the outer wheel is fee to rotate then fine, but it it was touching the floot the wheel-pair would stop.

Quays to the left; quays to the right. It's a paradox.

[SpeckledJim]

Is this a wind-up?

[thegreenhell]

SpeckledJim said:

Is this a wind-up?

Surely it would be the same whether the wheel was motor-driven or clockwork?

[VinceFox]

[mrmr96]

OldJohnnyYen said:

This is frying my brain, I can't think of a single way of explaining this properly.

http://io9.com/the-wheel-paradox-that-stumped-aris...

The link itself explains it in two different ways. This is not a paradox. Nor is it science.

[Russian Rocket]

think of the smaller wheel being on a conveyor belt.........

[tapkaJohnD]

It is not a paradox, but a false argument, because it uses a false premise, and incomplete data. It presumes that the smaller wheel travels at the same speed as the larger. What the small wheel does is to travel a shorter distance, in the same time, AT A SLOWER SPEED, so that it completes a complete turn in the same time as the larger wheel.

John

[Thorodin]

I think the inner wheel travels at exactly the same speed as the outer wheel, but in a linear direction. The reference point on the circumference of the inner wheel does not follow a circular track like the reference point on the outer wheel, more like the longer curved side of an ellipse.
Consider the analogy of the shortest distance between two points....