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:

$\overline{){\mathbf{n}}{\mathbf{=}}{\mathbf{d}}{\mathbf{\left(}}\frac{\mathbf{1}\mathbf{}\mathbf{r}\mathbf{e}\mathbf{v}}{\mathbf{C}}{\mathbf{\right)}}}$

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

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.

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