A centrifuge is a device used to separate materials by their masses. A sample in a centrifuge is rotated at high speeds along a circular path a distance of 10.0 cm from the center of the centrifuge. A centrifuge constantly accelerates a 1.00-gram sample from rest to a speed of 1,000 revolutions per minute in 1.00 seconds. Eventually, the sample reaches a speed 10.5 m/s. What is the magnitude and direction of the centripetal force acting on the sample

 F = 1.047 10⁻² N

Explanation:

Let's use kinematics to find the angular acceleration

             w = w₀ + α t

as for rest w₀ = 0

             w = α t

             α = w / t

let's reduce the magnitudes to the SI system

              w = 1000 rev / min (2π rad/ 1 rev) (1 min/ 60s) = 104.72 rad / s

              m = 1.00 g (1 kg / 1000 g) = 1,000 10⁻³ kg

              r = 10.0 cm (1 m / 100 cm) = 0.100 m

let's calculate

              α = 104.72 / 1

              α = 104.72 rad / s²

angular and linear variables are related

               a = α  r

               a = 104.72 0.100

               a = 10.47 m / s²

finally we substitute in Newton's second law

               F = 1 10⁻³ 10.47

               F = 1.047 10⁻² N

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