An ultracentrifuge accelerates from rest to 100,000 rpm in 3.00 min. (a) What is

ID: 1629852 • Letter: A

Question

An ultracentrifuge accelerates from rest to 100,000 rpm in 3.00 min.

(a) What is its angular acceleration in rad/s2?

__rad/s2

(b) What is the tangential acceleration (in m/s2) of a point 9.00 cm from the axis of rotation?

__m/s2

Question 2

With the aid of a string, a gyroscope is accelerated from rest to 18 rad/s in 0.35 s.

(a) What is its angular acceleration in rad/s2?

__ rad/s2

(b) How many revolutions does it go through in the process?

___rev

Question 3 With what angular speed does the Earth rotate about its axis?
___rad/s

PLEASE ANSWER ALL THE QUESTIONS AND DONT GIVE ANY WRONG ANSWERS THANKS FOR YOUR HEL!

(a) wi = 0

wf = 100,000 rpm = 100000 x 2pi rad / 60s

= 10471.98 rad/s

t = 3 x 60 = 180 sec

wf = wi + alpha t

10471.98 = 0 + 180 alpha

alpha = 58.2 rad/s^2

(b) a = alpha r = 58.2 x 0.09 = 5.24 m/s^2

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(a) 18 = 0 + 0.35 alpha

alpha = 51.4 rad/s^2

(b) wf^2 - wi^2 = 2 alpha theta

18^2 - 0^2 = 2 (51.4) (theta)

theta = 3.14 rad

revolutions = 0.50 rev

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3. T = 24 hrs = 24 x 3600 sec

w = 2pi / T = 7.27 x 10^-5 rad/s

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