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The centripetal force on a mass m moving on a circle of radius r can be written as which pair of equivalent expressions?
AFc = m*v/r and Fc = m*r*omega
BFc = m*v^2/r and Fc = m*r*omega^2
CFc = m*v^2*r and Fc = m*omega^2/r
DFc = m/v^2*r and Fc = m/(r*omega^2)
Answer & Solution
Correct answer: B. Fc = m*v^2/r and Fc = m*r*omega^2
1. Newton's second law gives Fc = m * ac, and centripetal acceleration is either v^2/r or r*omega^2.
2. Substituting the first form of ac gives Fc = m*v^2/r.
3. Substituting the second form of ac gives Fc = m*r*omega^2.
4. The other listed pairs change the power of v or omega, or move the radius to the wrong side of the expression, so they cannot come from substituting either form of centripetal acceleration into Fc = m*ac.
_Source: OpenStax College Physics (CC BY 4.0), Ch 6 "Uniform Circular Motion and Gravitation", section 6.3 Centripetal Force_
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