Question

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

(a)

What is its angular acceleration in rad/s²?

__________ rad/s^2

(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

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!