# A spot of paint on a bicycle tire moves in a circular path of radius 0.27 m. When the spot has...

## Question:

A spot of paint on a bicycle tire moves in a circular path of radius {eq}0.27 \ m {/eq}.

When the spot has traveled a linear distance of {eq}2.18 \ m {/eq}, through what angle has the tire rotated? (answer in radians.)

## Relation Between Arc and Radius

When an object moves on a circular path, the relation between the traveled and radius of the circle is

{eq}\begin{align} \theta = \frac{s}{r} \end{align} {/eq}

Where s is the arc length, r is the radius and {eq}\theta {/eq} is the angle swept.

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Data Given

• Radius of the path {eq}r = 0.27 \ \rm m {/eq}
• Length of the arc traveled {eq}s = 2.18 \ \rm m {/eq}

Let us draw a diagram

Arc and...