A ceiling fan is spinning with an angular velocity of +10RAD /s. It then comes to a stop over a brief period of time. During this time, its angular displacement is +8.7RAD. The blades of the fan extend 0.9 m from the center.
(a) Determine the average angular acceleration.
(b) Determine the time during which it comes to rest.
(c) How far (in meters) does the tip of each blade travel during this time?
(a) Initial angular velocity, w0 = 10 rad/s
angular displacement, theta = 8.7 rad.
use the expression -
w^2 = w0^2 + 2*alpha*theta
put the values -
0 = 10^2 + 2*alpha*8.7
=> alpha = -10^2 / (2*8.7) = - 5.75 rad/s^2
(b) use the expression -
w = w0 + alpha*t
=> 0 = 10 - 5.75*t
=> t = 10/5.75 = 1.74 s.
(c) 2*pi radian = 360 deg. = circumference of the circle = 2*pi*r
=> 1 radian = 2*pi*r / (2*pi) = r meter = 0.9 meter
so 8.7 radian = 8.7*0.9 = 7.83 m.
So, the distance travelled by the tip of the blade = 7.83 m.
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