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Each blade of a fan has a radius of 11 inches. If the fan’s rate of turn is 1440o /sec, find the following. (a) The angular speed in units of radians/sec. (b) The linear speed in units of inches/sec of a point on the outer edge of the blade.

Respuesta :

JhoanEusse

Answer:

a) 24.43 radians per second

b) 268.73 inches per second

Explanation:

a) The angular speed of the fan on Celsius degrees/second is 1400, so we should convert that value to radians using the fact that 2π rad = 360 °C:

[tex]\omega = 1400\frac{C}{s}=1400\frac{C}{s}*\frac{2\pi\,rad}{360\,C} [/tex]

[tex]\omega = 1400\frac{C}{s}=24.43\frac{rad}{s} [/tex]

b) Linear speed on a point of the blade is related with angular speed of the fan by the equation

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

with v linear speed, ω angular speed and r the radius of the blades. So:

[tex]v=(24.43\frac{rad}{s})(11 in) [/tex]

Radians isn't really a unity; it is dimensionless so we can put it or not. So:

[tex]v=268.73\frac{in}{s} [/tex]

pristina

The angular speed of the fan in radians/sec is [tex]24.434\, radians/s[/tex].

The linear speed of the fan in inches/sec is [tex]268.774 \,inches/s[/tex]

Given that the fan rotates at a rate of [tex]1440^{\circ} \,/s[/tex].

  • We know that, [tex]360^\circ = 2\pi \,radians[/tex]
  • Therefore, [tex]1440^\circ = \frac{2\pi}{360^\circ} \times1440^\circ \,radians = 25.1327 \, radians[/tex]
  • ie; angular distance is, [tex]\theta = 24.434\,radians[/tex]
  • Therefore, angular speed [tex]\omega = \theta /s = 24.434\, radians/s[/tex]

Now to find the linear speed, we can use the formula;

  • [tex]v=r\omega[/tex]

Given the length of the blade, ie; the radius of the fan [tex]r = 11\, inches[/tex].

  • Therefore, [tex]v=11\, inches \times 24.434 radians/sec = 268.774\, inches/s[/tex]

Learn more about angular speed here:

https://brainly.com/question/10229393

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