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For a point at radius r on a spinning object with angular velocity omega, what is the relationship between its linear speed v, r, and omega?
Av equals omega divided by r
Bv equals r divided by omega
Cv equals r plus omega
Dv equals r times omega
Answer & Solution
Correct answer: D. v equals r times omega
1. Linear speed and angular velocity are related through the arc length equation, arc length equals radius times rotation angle.
2. Dividing both sides by time turns rotation angle per time into angular velocity, giving v equals r times omega.
3. Omega divided by r or r divided by omega would give units that do not match a speed built from a radius and an angular velocity.
4. Adding r and omega would combine a length and an angle rate directly, which cannot represent a speed either.
_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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