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likoan [24]
3 years ago
5

Find the length l of one "arch" of this cycloid, that is, find the distance traveled by a small stone stuck in the tread of a ti

re of radius r during one revolution of the rolling tire.
Physics
2 answers:
Evgesh-ka [11]3 years ago
4 0

Answer: L = 2*R*π

Explanation: Considering the case where no other forces or effects are happening (Sliding, deformation, etc) The path that the rock does inside of a circular object is equal to the perimeter of the circular object, in this case, a rolling tire.

Then if the radius of the tire is R; the perimeter of the tire is equal to:

p = 2*R*π  

And for one revolution of the tire, the length of the arc that the rock travels is equal to the perimeter; so we have:

L = P = 2*R*π

Marat540 [252]3 years ago
3 0

If there is no slipping or skidding going on, then for each revolution, the tire rolls along the ground a distance equal to the tire's circumference.

Circumference of the tire = 2 · π · Radius .

During the same revolution, the small stone stuck in the tread travels in a big semicircular arc that's  <em>(2 · π · r)</em> long.  (roughly 6.28r)

 

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