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Problem: An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s2 ?(b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation?(c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm?(d) What is the total distance traveled by point 9.5 cm from the axis of rotation of the ultracentrifuge? 

FREE Expert Solution

Rotational kinematic equations:

ωf=ω0 + αtθ=12(ω0+ωf)tθ=ω0t +12αt2ωf2=ω02+2αθ

Tangential acceleration:

at=αr

Centripetal acceleration:

ac=ω2r

(a)

First, we'll convert the angular velocity to rad/s.

100000revmin×2π rad1 rev×1 min60 s=10472 rad/s

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Problem Details

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. 

(a) What is the average angular acceleration in rad/s2 ?

(b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation?

(c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm?

(d) What is the total distance traveled by point 9.5 cm from the axis of rotation of the ultracentrifuge? 

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