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An electric ceiling fan is rotating about a fixed axis with an initial angular velocity magnitude of 0.240 rev/s. The magnitude of the angular acceleration is 0.917 rev/s^2. Both the the angular velocity and angular acceleration are directed counterclockwise. The electric ceiling fan blades form a circle of diameter 0.720 m. a) Compute the fan's angular velocity magnitude after time 0.203 s has passed.Compute the fan's angular velocity magnitude after time 0.203 s has passed. Express your answer numerically in revolutions per second. b) What is the tangential speed vt of a point on the tip of the blade at time t = 0.203 s? Express your answer numerically in meters per second. c) Calculate the magnitude at of the tangential acceleration of a point on the tip of the blade at time t= 0.203 s. Express the acceleration numerically in meters per second squared.

Respuesta :

Explanation:

Given that,

Angular velocity = 0.240 rev/s

Angular acceleration = 0.917 rev/s²

Diameter = 0.720 m

(a). We need to calculate the angular velocity after time 0.203 s

Using equation of angular motion

[tex]\omega_{f}=\omega_{i}+\alpha t[/tex]

Put the value in the equation

[tex]\omega_{f}=0.240+0.917\times0.203[/tex]

[tex]\omega_{f}=0.426\ rev/s[/tex]

The angular velocity is 0.426 rev/s.

(b). We need to calculate the tangential speed of the blade

Using formula of  tangential speed

[tex]v= r\omega[/tex]

Put the value into the formula

[tex]v = \dfrac{0.720 }{2}\times0.426\times2\pi[/tex]

[tex]v=0.963\ m/s[/tex]

The tangential speed of the blade is 0.963 m/s.

(c). We need to calculate the magnitude at of the tangential acceleration

Using formula of tangential acceleration

[tex]a_{t}=r\alpha[/tex]

Put the value into the formula

[tex]a_{t}=0.36\times0.917\times2\pi[/tex]

[tex]a_{c}=2.074\ m/s^2[/tex]

The tangential acceleration is 2.074 m/s².

Hence, This is required solution.

onyebuchinnaji

(a) The final angular velocity of the fan blade is 2.68 rad/s.

(b) The tangential speed of the blade at a point on the tip of the blade is 0.965 m/s.

(c) The tangential acceleration of the blade is 2.07 m/s².

Final angular velocity of the fan blade

The final angular velocity of the fan blade is calculated as follows;

ωf = ω₀ + αt

ωf = (0.24 x 2π) + (0.917 x 2π)(0.203)

ωf = 2.68 rad/s

Tangential speed of the blade

The tangential speed of the blade at a point on the tip of the blade is calculated as follows;

v = ωf x (0.72/2)

v = 2.68 x 0.36

v = 0.965 m/s

Tangential acceleration

The tangential acceleration is calculated as follows;

[tex]a_t =\alpha r\\\\\a_t = (0.917 \times 2\pi) \times 0.36\\\\a_t =2.07 \ m/s^2[/tex]

Learn more about tangential speed here: https://brainly.com/question/19660334

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