Which wheel moves faster: the smaller or larger one?

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SUMMARY

The discussion centers on the speed comparison between wheels of different sizes on a moving cart. It is established that while all wheels move at the same linear speed (e.g., 20 mph) when rigidly attached to the cart, their rotational speeds differ. Specifically, the smaller wheel rotates faster than the larger wheel due to its smaller radius, which results in a higher RPM (revolutions per minute). The key takeaway is that linear speed remains constant across all wheels, but rotational speed is inversely proportional to the wheel's radius.

PREREQUISITES
  • Understanding of linear speed and rotational speed concepts
  • Basic knowledge of physics, particularly circular motion
  • Familiarity with the formula for circumference (C = 2πr)
  • Concept of revolutions per minute (RPM) in mechanical systems
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  • Research the relationship between linear speed and rotational speed in mechanical systems
  • Study the physics of circular motion and its applications
  • Explore the implications of wheel size on vehicle dynamics
  • Learn about the effects of wheel size on traction and performance in vehicles
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This discussion is beneficial for physics students, mechanical engineers, and anyone interested in understanding the dynamics of wheel motion and vehicle performance.

TheMathMan
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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.
 
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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.
 
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.
 
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.
 
TheMathMan said:
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.
 
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