An ultracentrifuge accelerates from rest to 100,000 rpm in 2.50 min.
What is its angular acceleration in rad/s2?
What is the tangential acceleration, in m/s2, of a point 10.80 cm from the axis of rotation?
What is the radial acceleration, in m/s2, of this point at full rpm?
Express this radial acceleration as a multiple of 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 -
10470 rad/s = 0 rad/s + α*150s
=> α = 69.8 rad/s^2
(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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