Physics

Problem

A potter’s wheel is a uniform circular disc of radius

0.40\,\text{m}

. A point on the rim is observed to move through a linear distance of

15\,\text{m}

along the circumference. (a) Calculate the angular displacement of the point in radians. (b) Express the angular displacement obtained in part (a) in (i) revolutions and (ii) degrees. (c) Explain, with reasoned arguments based on the relationship between arc length and angle, why the linear distance travelled along the circumference of a given wheel is directly proportional to the number of complete revolutions executed by the wheel.

Intuitive explanation

Angular displacement connects the arc length a point travels to how far around the circle it rotates—the key is the relationship $s = r\theta$ , where $s$ is arc length, $r$ is radius, and $\theta$ is angle in radians. Once you find the angle in radians, converting to revolutions and degrees is just a matter of knowing the conversion factors ( $2\pi$ radians per revolution, $360°$ per revolution). Part (c) asks you to explain why this relationship means distance and revolutions are proportional—think about what happens when you rearrange the arc-length formula to isolate the number of complete rotations.

Intuitive explanation

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