Explanation
Two vectors ¯A and ¯B lie in a plane. Another vector ¯C lies outside this plane, then the resultant of the three vectors (¯A+¯B+¯C) :
The observer will see only four spokes if the difference of angular
displacements of wheel 1 \& 2 is
n2π4=nπ2 Difference in angular displacement = (8rev/min - 6rev/min)\times t =2×2π×t=4π×t(tinminutes) The least time after which observer will see only four spokes is given by
4π×t=(1)π2 \therefore t= 1/8 min Therefore no of times observer will see only four spokes in a min= 8We can also think of this in following way: No of times observer will see only four spokes in a time period will be the value of n as it will tell us the number of (π2) degrees rotations that the wheels have
taken relative to each other. And everytime they takes a π2 degree rotation relative to each other
observer will see only four spokes once.
In 1 min 2×2π=4π=8π2 . Therefore 8 times a min.
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