Question

How fast (in rpm) must a centrifuge rotate if a particle7.0cm from the axis of rotation is to experience an acceleration of 100000 m/s2?

Answer 1

w = 3.6087 10⁶ rpm

Step-by-step explanation:

The centripetal acceleration is

a = v²/r

where r is the distance from the center of rotation and v is the magnitude of the velocity

let's reduce to the SI system

r = 7.0 cm (1m / 100cm) = 0.070 m

the angular and linear variables are related

v = w r

we substitute

a = w² r

w =
`\sqrt{(a)/(r) }`

w =
`\sqrt{ (100000^2)/(0.07) }`

w = 3.779 10⁵ rad / s

let's reduce to rpm

w = 3.779 10⁵ rad / s (1rev / 2pi rad) (60 s / 1min)

w = 3.6087 10⁶ rpm