A bolt located 50 mm from the center of an automobile wheel is tightened by applying the couple shown for 0.10 s. Assuming that the wheel is free to rotate and is initially at rest, determine the resulting angular velocity of the wheel. The wheel has a mass of

Question

A bolt located 50 mm from the center of an automobile wheel is tightened by applying the couple shown for 0.10 s. Assuming that the wheel is free to rotate and is initially at rest, determine the resulting angular velocity of the wheel. The wheel has a mass of 19 kg and has a radius of gyration of 250 mm.

Accepted Answer

Moment of inertia.[latex]\overline { I } =m{ k }^{ 2 }=\left( 19kg ight) { \left( 0.25m ight) }^{ 2 }=1.1875kg-{ m }^{ 2 }[/latex]

Applied couple. [latex]M=\left( 100N ight) \left( 0.460m ight) =46N-m[/latex]

Moments about axle:[latex]0+Mt=\overline { I } { \omega }[/latex]

[latex]\ 0+\left( 46N-m ight) \left( 0.10s ight) =\left( 1.1875kg.{ m }^{ 2 } ight) \omega[/latex]

[latex] \ \omega =3.87rad/s[/latex]

Question : A bolt located 50 mm from the center of an automob...