A centrifuge whose maximum rotation rate is w = 10,000 revolutions per minute (r

Question

A centrifuge whose maximum rotation rate is w = 10,000 revolutions per minute (rpm) can be brought to rest in a time t = 3.02s. Assume constant angular acceleration.

(a) What is the angular speed, in SI units, just before it begins decelerating?

(b) What is the angular acceleration in SI units?

(c) How far (m) does a point R = 8:13 cm from the center travel during the deceleration?

(d) What is the radial component of acceleration (m/s2) of the point just as the centrifuge begins its deceleration?

(e) What is the tangential component of acceleration (m/s2) of the point just as the centrifuge begins its deceleration?

Explanation / Answer

a)angular speed max.=2*pi*10^4/60 radians/sec=1047.2 radians/sec b)angular acceleration= -1047.2/3.02=-346.75 radians/s^2 c)(1047.2^2)/2/346.75=1581.3 radians so distance travelled= 1581.3*8.13=128.55 metres d)radial acceleration =rw^2=0.0813*1047.2^2=89155 m/s^2 e)v=rw, so dv/dt=rdw/dt=0.0813*-346.75=28.2m/s^2

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