Respuesta :
Answer:
(A). the angular velocity of fan is 0.380 rev/s.
(B). The number of revolution is 0.059 rad.
(C). The tangential speed of the blade is 0.907 m/s.
(D). The tangential acceleration of the blade is 2.10 m/s²
Explanation:
Given that,
Initial angular velocity = 0.200 rev/s
Angular acceleration = 0.883 rev/s²
Diameter = 0.760 m
Time = 0.204 s
(A). We need to calculate the angular velocity of fan
Using equation of angular motion
[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]
Put the value into the formula
[tex]\omega_{f}=0.200+0.883\times0.204[/tex]
[tex]\omega_{f}=0.380\ rev/s[/tex]
(B). We need to calculate the number of revolution
Using formula of angular displacement
[tex]\theta=\omega_{i}t+\dfrac{1}{2}\alpha t^2[/tex]
Put the value into the formula
[tex]\theta=0.200\times0.204+\dfrac{1}{2}\times0.883\times(0.204)^2[/tex]
[tex]\theta=0.059\ rad[/tex]
(C). We need to calculate the tangential speed of the blade
Using formula of speed
[tex]v=\dfrac{d}{2}\omega_{f}[/tex]
Put the value into the formula
[tex]v=\dfrac{0.760}{2}\times0.380\times2\pi[/tex]
[tex]v=0.907\ m/s[/tex]
(D). We need to calculate the tangential acceleration of the blade
Using formula of tangential acceleration
[tex]a_{t}=\alpha r[/tex]
Put the value into the formula
[tex]a_{t}=0.883\times0.38\times2\pi[/tex]
[tex]a_{t}=2.10\ m/s^2[/tex]
Hence, (A). the angular velocity of fan is 0.380 rev/s.
(B). The number of revolution is 0.059 rad.
(C). The tangential speed of the blade is 0.907 m/s.
(D). The tangential acceleration of the blade is 2.10 m/s²
