To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.
Here,
M = Mass
R = Radius of the hoop
The precession frequency is given as
Here,
M = Mass
g= Acceleration due to gravity
d = Distance of center of mass from pivot
I = Moment of inertia
= Angular velocity
Replacing the value for moment of inertia
The value for our angular velocity is not in SI, then
Replacing our values we have that
The precession frequency is
Therefore the precession period is 5.4s
If this case could ever happen, the speed would follow from this formula:
with f the frequency and lambda the wavelength. We are give a wavelength of 10m. The frequencies of the visible light can range between 400 to about 790 Terahertz, so let us pick a middle point of 600 THz ("green-ish") as a "representative."
The speed of such a wave would have to be 6e+15 m/s (which would be 7 orders of magnitude higher than the universal speed of light constant)
The displacement of a moving object is the straight-line distance between the place it starts from and the place where it stops.
The displacement of anything moving along a circular track depends on how far around it goes before it stops. The greatest displacement it can possibly have is the diameter of the track ... 100m on this particular one ... because that's as far apart as two places on a circle can ever be.
The most interesting case is when the object goes around the circle exactly once. Then it stops at the same place it started from, the distance between the starting point and ending point is zero, and after all that motion, the displacement is zero.
