A centrifuge rotor rotating at 9500 rpm is shut off and is eventually brought un

Question

A centrifuge rotor rotating at 9500 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.81 m?N . Part A If the mass of the rotor is 4.01 kg and it can be approximated as a solid cylinder of radius 0.0630 m , through how many revolutions will the rotor turn before coming to rest? Express your answer to three significant figures. N = nothing revolutions Request Answer Part B How long will it take? Express your answer to three significant figures and include the appropriate units. t =

Explanation / Answer

here,

intial angular speed , w0 = 9500rpm = 994.3 rad/s

mass , m = 4.01 kg

radius ,r = 0.063 m

torque = 1.81 mN = 0.00181 N

let the magnitude of angular accelration be alpha

equating the torque

I * alpha = T

0.5 * m * r^2 * alpha = T

0.5 * 4.01 * 0.063^2 * alpha = 0.00181

alpha = 0.23 rad/s^2

a)

the angle covered , theta = w0^2 /2alpha

theta = 994.3^2 /(2 * 0.23)

theta = 2.17 * 10^6 rad

the number of revolution , N = theta /2pi

N = 2.17 * 10^6 /( 2*pi)

N = 3.46 * 10^5 revolutions

b)

let the time taken be t

0 = w0 + alpha * t

0 = 994.3 - 0.23 * t

t = 4323 s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.