Builders Use Leveling Instrument

Builders use a leveling instrument with the beam from a fixed helium–neon laser reflecting in a horizontal plane from a small flat mirror mounted on an accurately vertical rotating shaft. The light is sufficiently bright and the rotation rate is sufficiently high that the reflected light appears as a horizontal line wherever it falls on a wall.
(a) Assume the mirror is at the center of a circular grain elevator of radius R. The mirror spins with constant angular velocity wm.
Find the speed of the spot of laser light on the wall.
(b) What If? Assume the spinning mirror is at a perpendicular distance d from point O on a flat vertical wall. When the spot of laser light on the wall is at distance x from point O, what is its speed?

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