A heavy flywheel rotating counterclockwise about its middle at an original speed of 157.1 rad/s is slowing down because of friction in its bearings. a. If its acceleration is constant at 1.785 rad/s², find its angular velocity at the end of 1.00 minute. b. The flywheel is 5.50 m in diameter and has a mass of 985 kg. If the flywheel resembles a uniform disk, find the torque applied by friction.

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aristocles aristocles · Answer 1 · 2020-04-07T20:02:52+02:00

Answer:

Part a)

Final angular speed of the wheel is

[tex]\omega_f = 50 rad/s[/tex]

Part b)

torque on the wheel is given as

[tex]\tau = 6648.3 N m[/tex]

Explanation:

Part a)

As we know that initial angular speed of the flywheel is

[tex]\omega_i = 157.1 rad/s[/tex]

angular deceleration of the flywheel is given as

[tex]\alpha = - 1.785 rad/s^2[/tex]

Final angular speed of the fly wheel is given as

[tex]\omega_f = \omega_i + \alpha t[/tex]

[tex]\omega_f = 157.1 + (-1.785)(60)[/tex]

[tex]\omega_f = 50 rad/s[/tex]

Part b)

As we know that moment of inertia of the disc is given as

[tex]I = \frac{1}{2}mR^2[/tex]

so we have

[tex]I = \frac{1}{2}(985)(\frac{5.50}{2})^2[/tex]

[tex]I = 3724.5 kg m^2[/tex]

So torque on the wheel is given as

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

[tex]\tau = 3724.5(1.785)[/tex]

[tex]\tau = 6648.3 N m[/tex]