The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The 50-kg rotor, which has a centroidal radius of gyration of 180 mm, then coasts to rest. Knowing that kinetic friction results in a couple of magnitude 3.5 N m⋅ exerted on the rotor, determine

Question

The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The 50-kg rotor, which has a centroidal radius of gyration of 180 mm, then coasts to rest. Knowing that kinetic friction results in a couple of magnitude 3.5 N m⋅ exerted on the rotor, determine the number of revolutions that the rotor executes before coming to rest.

Accepted Answer

[latex]\overline { I } =m{ \overline { k } }^{ 2 } [/latex]

=[latex]\left( 50 ight) { \left( 0.180 ight) }^{ 2 } [/latex]

[latex]=1.62kg.{ m }^{ 2 } M=\overline { I } \alpha :3.5N.[/latex]

[latex]m=\left( 1.62kg.{ m }^{ 2 } ight) \alpha [/latex]

[latex]\alpha =2.1605rad/{ s }^{ 2 }[/latex] (deceleration)

[latex]{ \omega }_{ 0 }=3600rpm\left( \frac { 2\pi }{ 60 } ight)[/latex]
=[latex]120\pi \quad rad/s[/latex]

[latex]{ \omega }^{ 2 }={ \omega }_{ 0 }^{ 2 }+2\alpha heta [/latex]

[latex]0={ \left( 120\pi \quad rad/s ight) }^{ 2 }+2\left(-2.1605rad/{ s }^{ 2 } ight) heta [/latex]

[latex] heta =32.891 imes { 10 }^{ 3 }rad[/latex]

[latex]=5235.26rev[/latex]

or [latex] heta=5230rev[/latex]

Question : The rotor of an electric motor has an angular velocity of 36...

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