A fairground ride spins its occupants inside a flying saucer-shaped container. If the horizontal circular path the riders follow has a 6.3 m radius, if the riders is subjected to a centripetal acceleration 1.3 times that due to gravity, what is the spinning speed in unit of revolutions per minute? Use g = 9.8 m/s^{2}.
Solution)
Given,
Radius, r=6.3 m
Centripetal acceleration, a=1.3*g
We know, centripetal acceleration, a=rw^2
So, 6.3*w^2=1.3*9.8
Angular velocity, w= 1.422 rad/s
We also know, Time period, T for one revolution=2pi/w=2*pi/1.422= 4.41 sec
Now, spinning speed in rev/min=60/4.41= 13.58 rev/min (Ans)
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