Question

# An ultracentrifuge accelerates from rest to 100,000 rpm in 2.50 min. (a) What is its angular...

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.50 min.

(a)

What is its angular acceleration in rad/s2?

(b)

What is the tangential acceleration, in m/s2, of a point 10.80 cm from the axis of rotation?

_________ m/s2

(c)

What is the radial acceleration, in m/s2, of this point at full rpm?

__________ m/s2

(d)

Express this radial acceleration as a multiple of g.

_________ g

(a) Convert revolution per minute (rpm) into radian per sec.

ω = 100000 rev/min * 2π rad/rev * 1min/60s = 10470 rad/s

t = 2.50 min = 150 s

Use the expression -

ω = ωo + at

Put the values -

(b) Tangential acceleration, a_t = αr

= 69.8 * 0.108 m = 7.54 m/s^2

(c) Radial acceleration, a_r = ω²r

= (10470 rad/s)^2 * 0.1080 m = 1.18 x 10^7 m/s^2

(d) As a multiple of 'g', this becomes (1.18 x 10^7) / g = (1.18 x 10^8) / 9.8 =  1208067 "g"s (Answer)

Hope, you understand the solution!

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