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What is the angular speed of the tires?

A bicycle with 0.80-m-diameter tires is coasting on a level road at 5.6 m/s. A small blue dot has been painted on the tread of the rear tire.

Also, What is the speed of the blue dot when it is 0.80 m above the road? and What is the speed of the blue dot when it is 0.40m above the road?

Posted 263 day ago

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Answers (2)

Correction:
In the first line of Tom's answer, "Diameter" should be "Circumference". The calculations are correct, only the word is incorrect. I could not get the edit function to Save.

Posted 260 day ago

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Revolutions / second = Speed of Center / Diameter
= (5.6 m / s) / ((2 x Pi ) x Radius)
Angular speed, W = (2 x Pi) x (Rev / s) radians, since there are 2 Pi radians for each revolution
= (5.6 m / s) / radius
= (5.6 m / s) / 0.4 m
ANSWER W = 14 rad / s


Speed = W x Distance from center of rotation, the point of contact on the ground.
= (14 rad / s) x 0.8 m
ANSWER Speed = 11.2 m / sec when dot is 0.8 m above the ground.


By geometry, the distance of the blue dot from the ground when it is 0.4 m above the ground is
(square root of 2) x radius = 1.414 x 0.4 m
= 0.5656 m
Speed = W x distance
= (14 rad / s) x 0.5656 m
ANSWER Speed = 7.92 m / s (approximated irrational number from sqrrt of 2)




Posted 262 day ago

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