Question

A wheel of radius R is fixed at height h in the y-z plane with the ability to rotate about its center. a mass is attached to a point on the outside of the wheel by a string, causing it to rotate clockwise. the S' frame is painted on the wheel and the system itself is in the S frame. when the mass is released from rest S' coincides with S. assuming that as the wheel rotates the S' frame remains aligned with the S frame, find an expression for position, velocity, and acceleration of a point p located on the edge of the wheel. The wheel rotates in the y-z plane.

Answer 1

given wheel radius R
height h in yz plane
ability to rotate about its center

mass attached to it outside the wheel with a string such that the wheel begins to rotate clockwise

S' frame is painted on the wheel and the wheel itself is in S frame
before motion both the frames coincide

as the wheel rotates the center of the two frames keep aligned
hence consider a point P on the periphery of the wheel

in S' frame
position r' = Rcos(phi)j' + Rsin(phi)k'
where j' and k' are unit vectors in S' frame of reference
so
velocity v' = 0
where phi is the initial angle the point P makes with horizontal axis parallel to the disc
acceleration
a' = 0
for S frame
r = Rcos(-wt + phi)j' + Rsin(-wt + phi)k'
v = Rwsin(-wt + phi)j'- Rwcos(-wt + phi)k'
a = -Rw^2cos(-wt + phi)j' - Rw^2sin(-wt + phi)