Converting Between Linear & Rotational Video Lessons

Concept

Problem: A spot of paint on a bicycle tire moves in a circular path of radius 0.33 m.  When the spot has traveled a linear distance of 1.76 m, through what angle has the tire rotated? Give your answer in radians.

FREE Expert Solution

The distance traveled by the spot of paint on the tire in one complete revolution is equal to the circumference of the tire given by:

$\overline{){\mathbf{C}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi }}{\mathbf{r}}}$

The number of revolutions, n for the tire to cover the distance d is expressed as:

From the first equation, C = (2π)(0.33) = 2.073 m

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Problem Details

A spot of paint on a bicycle tire moves in a circular path of radius 0.33 m.  When the spot has traveled a linear distance of 1.76 m, through what angle has the tire rotated? Give your answer in radians.