Instantaneous angular speed omega = lim_delta t rightarrow delta theta/delta t =
ID: 1553412 • Letter: I
Question
Instantaneous angular speed omega = lim_delta t rightarrow delta theta/delta t = d theta/d t Instantaneous angular acceleration alpha = lim_delta t rightarrow 0 delta omega/delta t = d omega/d t theta = theta_0 + omega t theta = theta_0 + omega_0t + 1/2 alpha t^2 omega = omega_0 + a t alpha = const or average omega^2 = omega_0^2 + 2a delta theta omega = 1/2 () if alpha = A hard drive is spinning at 7200 rpm and suddenly it loses its power. And with 2.0 ms. the spinning stops. 1) What is the angular acceleration while it is stopping? 2) What is average angular speed? 3) What is the angular displacement in revolutions from spinning to when it stops? (imagine a particle on the disc, how much revolution will it take for it to stop. 1 rev = 2 pi 4) What is the total distance (not displacement) the particle from spinning to when it stops? 5) A dust particle is sitting on the hard drive platter. When it is linear speed?Explanation / Answer
a)
from
W=Wo+alpha*t
0=(7200*2pi/60)-alpha*(2*10-3)
alpha=3.77*105 rad/sec2
b)
average angular speed
Wavg=(W+WO)/2=(7200+0)*(2pi/60)/2=377 rad/sec
c)
from
theta=thetao+Wot+(1/2)*alpha*t2
theta =0+(7200*2pi/60)*(2*10-3)-(1/2)*(3.77*105)*(2*10-3)2
theta=0.754 rad
in revolutions
theta =0.754/2pi=0.12 rev
d)
radius of hard drive is needed for this ,typically it 8.9 cm
d=theta*r=0.089*0.754=0.067 m