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As an object moves along a circular arc, its rotation angle is defined as which ratio?
AThe arc length divided by the radius of curvature
BThe radius of curvature divided by the arc length
CThe arc length divided by the full circumference
DThe linear speed divided by the radius of curvature
Answer & Solution
Correct answer: A. The arc length divided by the radius of curvature
1. The rotation angle of an object moving along a circular path is defined as the arc length it sweeps out divided by the radius of curvature of that path.
2. This ratio is measured in radians, since one full revolution sweeps out an arc length equal to the circumference, 2 pi r, giving a rotation angle of 2 pi rad.
3. Dividing the radius by the arc length inverts the definition and does not give the rotation angle.
4. Dividing arc length by the full circumference gives the fraction of a turn completed, and linear speed divided by radius gives angular velocity, not rotation angle.
_Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.1 Rotation Angle and Angular Velocity_
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