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)

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