Answer:
(a) 18.75 rad/s²
(b) 14920.78 rev
Explanation:
(a)
First we find the acceleration of the centrifuge using,
a = (v-u)/t......................... Equation 1
Where v = final velocity, u = initial velocity, t = time.
Given: v = 150 m/s, u = 0 m/s ( from rest), t = 100 s
Substitute into equation 1
a = (150-0)/100
a = 1.5 m/s²
Secondly we calculate for the angular acceleration using
α = a/r..................... Equation 2
Where α = angular acceleration, r = radius of the centrifuge
Given: a = 1.5 m/s², r = 8 cm = 0.08 m
substitute into equation 2
α = 1.5/0.08
α = 18.75 rad/s²
(b)
Using,
Ф = (ω'+ω).t/2........................... Equation 3
Where Ф = number of revolution of the centrifuge, ω' = initial angular velocity, ω = Final angular velocity.
But,
ω = v/r and ω' = u/r
therefore,
Ф = (u/r+v/r).t/2
where u = 0 m/s (at rest), = 150 m/s, r = 0.08 m, t = 100 s
Ф = [(0/0.08)+(150/0.08)].100/2
Ф = 93750 rad
If,
1 rad = 0.159155 rev,
Ф = (93750×0.159155) rev
Ф = 14920.78 rev
