Physics

Problem

Which of the following statements correctly justifies why the centripetal force on a body of mass

m

moving with speed

v

in a circle of radius

r

is written as

F_c = m\,v^{2}/r

? a) Because centripetal acceleration is

a_c = v/r

, so applying

F = m a

directly yields

F_c = m v/r

. b) Because Newton’s second law relates force to mass times acceleration, and for uniform circular motion the acceleration toward the centre is

a_c = v^{2}/r

. c) Because the work done in one revolution equals the kinetic energy

\tfrac{1}{2} m v^{2}

; dividing this work by the path length

2\pi r

gives

F_c = m v^{2}/(2 r)

. d) Because the inward centripetal force simply balances an equal and opposite outward centrifugal force

m v^{2}/r

, leaving

m v^{2}/r

as each individual force.