The valve cap n a bicycle wheel is 12.5 in from the center of the wheel. From the position shown, the wheel starts to roll. After the wheel has turned 390°, how far above the ground is the valve cap? Assume that the outer radius of the tire is 13.375 in.

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Thanks!

1 Answer
Doug2100
Mar 6, 2018

19.625 in off the ground

Explanation:

Within the 390 degree rotation, the overall displacement is 30 degrees since after 360 degrees, the cap is back to the original spot on the wheel. Taking only the y-axis into account, the change in height of the valve cap is #12.5sin(30)=6.25#. Add this change to the initial height off the ground (the diameter of the wheel) and you will have the "net" height of the valve cap.

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