Calculate Initial Angular Speed of Fan | High to Low Button Pushed

AI Thread Summary
The discussion focuses on calculating the initial angular speed of a fan that decelerates from a high speed to a low speed after the LOW button is pressed. The fan's final angular speed is 98 rad/sec, and it decelerates at a rate of 42.3 rad/sec² over 1.83 seconds. Using these values, the initial angular speed can be determined through the kinematic equations for rotational motion. The radius of the fan blades is 0.62 meters, which is relevant for understanding the fan's physical dimensions but not directly needed for the speed calculation. The conversation emphasizes the straightforward nature of the calculation involved.
choole
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An electric fan is running on HIGH. After fan has been running of 13.2 minutes, the LOW button is pushed. The fan slows down to 98 rad/sec in 1.83 seconds. The blades of the fan have a radius of 0.62 meters and their deceleration rate is 42.3 rad/sec2.

What was the initial angular speed of the fan in rev/sec?
 
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look at the second omega and alpha... its only one step to the solution...

edit: does seem to belong there eh pete?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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