A table-top fan has radius of 0.5 m. It starts to rotate from rest to 800 rpm within 30 seconds. Determine: 1) the angular momentum 2) how many revolutions have it gone through after 2 minutes? 3) If the rotational inertia of each blade around the center is 0.3 kg.m^ 2, what is the magnitude of the torque provided by the motor of the fan, assuming no friction?

Question

contestada

Respuesta :

aristocles aristocles · Answer 1 · 2019-07-25T03:54:30+02:00

Answer:

Part a)

L = 25.13 kg m^2/s

Part b)

N = 3200 rev

Part c)

torque = 0.837 Nm

Explanation:

Part a)

As we know that angular frequency is given as

[tex]\omega = 2\pi f[/tex]

[tex]\omega = 2\pi(800/60)[/tex]

[tex]\omega = 83.77 rad/s[/tex]

now the angular momentum is given as

[tex]L = I\omega[/tex]

[tex]L = (0.3)(83.77)[/tex]

[tex]L = 25.13 kg m^2/s[/tex]

Part b)

angular acceleration of fan is given as

[tex]\alpha = 2\pi\frac{800/60}{30}[/tex]

[tex]\alpha = 2.79 rad/s^2[/tex]

total number of revolutions are

[tex]N = \frac{1}{4\pi}\alpha t^2[/tex]

[tex]N = \frac{1}{4\pi}(2.79)(120^2)[/tex]

[tex]N = 3200 rev[/tex]

Part c)

Torque is given as

[tex]\tau = I\alpha[/tex]

[tex]\tau = (0.30)(2.79) = 0.837 Nm[/tex]