I = Iring + Idisk
= (m/2)*r^2 + (m/2)*r^2 / 2
= ( 0.106/2) *0.27^2 + ( 0.106/2) *0.27^2 /2
I = 0.005795 kg .m^2
w = 510 rpm = 510 * 2pi / 60 rad/s = 53. 41 rad/s
a(t) = 1/2* t^2
and the angular velocity
w = * t
........................1
pi/2 = 1/2 t^2
pi = *t^2 ................2
from 1
53. 41 = *t
= 53.41 /t
put in 2
pi = (53.41 /t) *t^2
pi = 53.41 * t
t= pi / 53.41
= 53.41 / ( pi / 53.41)
= 53.41^2 / pi
T = I = 0.005795 * 908.020 =5.2619 N.m
answer
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