the length of each blade of a ceiling fan is 80 cm. What is the diameter of the ceiling fan?
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Answers
Answer:
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1.97m/s
Step-by-step explanation:
Explanation:
The initial angular velocity of the blades is:
\omega_i = 70 rev/min = (70 rev/min) (\frac{2\pi rad/rev}{60 s/min})=7.33 rad/sω
i
=70rev/min=(70rev/min)(
60s/min
2πrad/rev
)=7.33rad/s
The final angular velocity is
\omega_f = 0ω
f
=0
(since the blades come to a stop)
and the time taken is
t = 30 s
So, the angular acceleration of the blades is
\alpha = \frac{\omega_f-\omega_i}{t}=\frac{0-7.33 rad/s}{30 s}=-0.24 rad/s^2α=
t
ω
f
−ω
i
=
30s
0−7.33rad/s
=−0.24rad/s
2
Now we can find the angular velocity of a blade after a time t=10 s:
\omega = \omega_i + \alpha t = 7.33 rad/s +(-0.24 rad/s^2)(10 s)=4.93 rad/sω=ω
i
+αt=7.33rad/s+(−0.24rad/s
2
)(10s)=4.93rad/s
The distance of the tip of a blade from the centre is equal to half the diameter, so
r=\frac{80 cm}{2}=40 cm=0.40 mr=
2
80cm
=40cm=0.40m
so, the speed of the tip of a blade is
v=\omega r=(4.93 rad/s)(0.4 m)=1.97 m/sv=ωr=(4.93rad/s)(0.4m)=1.97m/s