A spot of paint on a bicycle tire moves in a circular path of radius 0.27 m. When the spot has traveled a linear distance of 2.18 m, through what angle has the tire rotated? Give your answer in radians.

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Linear distance= radians x radius

solve for radians

linear distance/ radius = radians

To find the angle in radians that the tire has rotated, we need to use the relationship between the linear distance traveled and the angle of rotation.

The formula to relate the linear distance (s) traveled along the circumference of a circle to the angle (θ) of rotation in radians is:

θ = s / r

where r is the radius of the circle.

In this case, the linear distance traveled is given as 2.18 m and the radius of the circular path is 0.27 m. Plugging these values into the formula, we get:

θ = 2.18 m / 0.27 m

Simplifying this division, we find:

θ ≈ 8.07 radians

Therefore, the tire has rotated through an angle of approximately 8.07 radians.