Calculating Radius from Angular and Tangential Acceleration in a Bicycle Wheel

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SUMMARY

The radius of a bicycle wheel can be calculated using the relationship between angular acceleration and tangential acceleration. Given an angular acceleration of 1.4 rad/s² and a tangential acceleration of 49 cm/s², the radius can be determined using the formula: tangential acceleration = angular acceleration × radius. By rearranging this equation, the radius is found to be 35 cm or 0.35 m. This straightforward calculation demonstrates the direct relationship between these two types of acceleration.

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A bicycle wheel has an angular acceleration
of 1.4 rad/s2.
If a point on its rim has a tangential accel-
eration of 49 cm/s2, what is the radius of the
wheel?
Answer in units of m.

I know that there should be some way to relate the angular acceleration and the tangential acceleration but I can't figure it out.

I tried to relate the angular acceleration to angular speed to then find delta theta so then I could plug into S=Rtheta. The only problem is that I don't have the angular speed. I know that there has to be an easy way to do this problem.


The Attempt at a Solution

 
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Welcome to PF!

Hail BoldKnight399! Welcome to PF! :smile:

(erm :redface: … tangential is more-or-less the opposite of centripetal :rolleyes:)
BoldKnight399 said:
… I know that there should be some way to relate the angular acceleration and the tangential acceleration but I can't figure it out.

cm/s2 = radian/s2 times cm/radian

(just like cm/s = radian/s times cm/radian :wink:).

So what is cm/radian in this case? :smile:​
 
knew it had to be simple and I was just missing it. Thank you!
 

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