LOL
valve straight down is stable (pendulum)
valve straight up is unstable (balancing pencil on nose)
I = mr^2 = 1.005(.36) (about .36)
for angle x in radians, restoring moment is about .005*9.81 x r
= .003*9.81 x
oh well call g = 10 instead of 9.81
= .03 x
.03x = -I alpha = -I omega^2 x
omega^2 = .03/.36 = 3/36
omega = (1/6) sqrt 3 = 2 pi/T
T = 12 pi/sqrt 3
check my arithmetic, use calculator (I did in head)
Not sure where to go with this problem, any help is appreciated!
A bike is turned upside down for repairs. The front wheel can be described as a hoop with
radius R=0.6 m and mass M=1.0 kg and a small point mass m=0.005 kg attached to the
perimeter to represent the valve for inflating the tire (see Fig. 1). We consider rotation of
the wheel about its frictionless axle.
(a) Describe the two equilibrium positions for the wheel and identify the one of these that
is a stable equilibrium.
(b) Calculate the period for small angle oscillations of the wheel about the stable
equilibrium.
Thanks in advance!
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