What is the speed of the tip of a blade 10 secs after the fan is turned off?
A ceiling fan with 83-cm-diameter blades is turning at 64 rpm. Suppose the fan coasts to a stop 28 sec after being turned off.
1) What is the speed of the tip of a blade 10 s after the fan is turned off?
2) Through how many revolutions does the fan turn while stopping?
The angular acceleration is negative because it goes from a high rpm to a low rpm.
Converting to radians/sec the intiial angular speed is found as follows;
64 rev/min X 2*pi radians/1 rev X 1 min/60 sec= 6.70 rad/sec
angular acceleration= change in ang speed/change in time
=( 0 – 6.70)/28= 0.239 rad/s^2
the angular speed after 10 seconds = 6.70-0.239t
= 6.70-.239(10)
= 4.31 rad/s
regular velocity = angular speed*r
= 4.31(0.83/2) = 1.787 m/s
note:I converted the diameter to meters
Number of revolutions = 1/2 angular accel *t^2
=.239/2*28^2= 93.88 radians
93.88 radians* 1 rev/(2*pi rad)= 14.9 rev
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