Question

An ultracentrifuge accelerates uniformly from rest to 100,000 rpm in 2.0 min. If this ultracentrifuge accelerates 7.0 seconds starting from rest, what is the magnitude of the centripetal acceleration in unit of gravitational acceleration g for your sample sitting at 5.0 cm from the center axis? Use g = 9.8 m/s².

Answer 1

here,

for time , t1 = 2 min = 120 s

the final angular speed , w1 = 100,000 rpm

w1 = 10466.7 rad/s

let the angular acceleration be alpha

using first equation of motion

w1 = 0 + alpha * t1

10466.7 = 0 + alpha * 120

alpha = 87.22 rad/s^2

for t2 = 7 s

the angular speed , w2 = 0 + alpha * t2

w2 = 0 + 87.22 * 7 rad/s

w2 = 610.6 rad/s

r = 5 cm = 0.05 m

the magnitude of the centripetal acceleration , ac = w^2 * r

ac = 610.6^2 * 0.05 m/s^2 = 1.86 * 10^4 m/s^2

ac = 1.9 * 10^3 g