A wagon wheel has eight spokes. It is rotating at a constant angular velocity. Four snapshots of the wheel are taken at the four times illustrated in Figure E.46. Let the sampling interval (time between snapshots) be 10 ms.
(a) In Case 1, what are the three lowest positive angular velocities (in revolutions per second, rps) at which it could be rotating?
(b) In Case 2, what are the three lowest positive angular velocities (in revolutions per second, rps) at which it could be rotating?
(a) The slowest possible (non-zero) rotation would be 1/16 of a revolution in one sampling time. That means one complete revolution in 160 ms which yields a rotation rate of 6.25 rps. The next slowest rotation rate would be 3/16 of a revolution in one sampling time which equates to 18.75 rps. The next one would be 5/16 of a revolution and 31.25 rps.
(b) The slowest possible (non-zero) rotation would be 1/8 of a revolution in one sampling time. That means one complete revolution in 80 ms which equates to a rotation rate of 12.5 rps. The next two lowest rates are 25 and 37.5 rps.
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