A circular disk of radius r is mounted on a shaft that pivots about a fixed
point O. The disk rolls without slipping on a circle of radius R. It rolls at a constant
speed and goes all the way around the circle once in a time τ. Assume the disk has
negligible thickness. You can use the fact that the length of the shaft is L = [tex]\sqrt{R^{2}-r^{2} }[/tex].
See Picture
a) Write the transformation tables between the frames.
b) Write ψ˙, ˙θ, and ϕ˙ in terms of R, r, and τ. Also, write sin θ and cos θ in terms
of r, R, and L.
c) Find IωB, the angular velocity of B with respect to I. Write your final
answer in terms of B-frame unit vectors.
d) Find IαB, where IαB = I d/dt (IωB). Write your final answer in terms of
B-frame unit vectors.
e) (Find I v Q/O, the inertial velocity of point Q relative to point O. Write your
final answer in terms of B-frame unit vector.
