Which wheel moves faster: the smaller or larger one?

[TheMathMan]

OK. Our department at college has a question... none of us are science teachers.

A tractor and cart, all with different sized wheels, which travels fastest?

The answers are available are for any of the wheels ( smallest to biggest) or for all being the same?

My argument is, if the tractor is moving at say 20mph then all the wheels are moving at 20mph?

I'm sure this is an easy question for this forum. I did search buit couldn't find anything this low level.

 

[future_think]

They would all be moving at the same speed. The rotation RPM (revolutions per minute) of the smaller tire would be higher then that of the larger.

 

[HallsofIvy]

Obviously, if all wheels are rigidly attached to the cart, they all move along the ground at the same speed as the cart. But their rotational speed differ.

If the cart is moving at v m/s, a wheel, of radius r m, must turn fast enough that, in one second, its circumference moves v meters. Since its circumference has length $2\pi r$, it moves through that length in one revolution. It will move v m in $v/(2\pi r)$ revolutions so to move at speed v m/s, it must rotate $v/(2\pi r)$ revolutions per second. Note that r is in the denominator so rotational speed is inversely proportional to radius.

 

[TheMathMan]

Thanks for the replies.

I assume the big difference in opinions on this is due to the wording of the question as to how you interpret "fastest".

So technically, if we were talking about rotational speed then it would be the smaller wheel moving fastest, but if we assume a mph then they'd be equal?

Bear in mind this is just from a pretty basic aptitude test, along with questions such as which number is missing from the sequence etc etc.

 

[future_think]

Thanks for the replies.

So technically, if we were talking about rotational speed then it would be the smaller wheel moving fastest, but if we assume a mph then they'd be equal?

That is correct.

If you assume the speed along the X axis (horizontal vector) then both are moving 20mph.
If you assume the speed of rotation then the smaller tire would be rotating faster.