Aspot of paint on a bicycle tire moves in a circular path of radius 0.29 m. when the spot has traveled a linear distance of 1.31 m, through what angle has the tire rotated? give your answer in radians.

First we need to calculate the perimeter of the tire. Given the radius, r=0.29 m, the perimeter is

This is the length of one complete revolution, and the angle that corresponds to this distance is . So, if we want to find what is the angle that corresponds to a distance of 1.31 m, we can set a simple proportion:

From which we find x, the angle through which the tire has rotated: