Question

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

(a)

What is its angular acceleration in rad/s^{2}?

__________ rad/s^2

(b)

What is the tangential acceleration, in m/s^{2}, of a
point 10.80 cm from the axis of rotation?

_________ m/s^{2}

(c)

What is the radial acceleration, in m/s^{2}, of this
point at full rpm?

__________ m/s^{2}

(d)

Express this radial acceleration as a multiple of
*g*.

_________ *g*

Answer #1

(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!

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.80
min.
(a)
What is its angular acceleration in rad/s2?
rad/s2
(b)
What is the tangential acceleration, in m/s2, of a
point 11.80 cm from the axis of rotation?
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(c)
What is the radial acceleration, in m/s2, of this
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m/s2
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