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A bar on a hinge starts from rest and rotates with an angular acceleration α = 15 + 9t, where α is in rad/s2 and t is in seconds. determine the angle in radians through which the bar turns in the first 3.91 s.

Respuesta :

As we know that angular acceleration is given by

[tex]\alpha = 15 + 9t[/tex]

[tex]\frac{dw}{dt} = 15 + 9t[/tex]

integrating both sides

[tex]w - 0 = 15t + 4.5 t^2[/tex]

again we can write

[tex]\frac{d\theta}{dt} = 15t + 4.5 t^2[/tex]

again integrating both sides

[tex]\theta = 7.5t^2 + 1.5t^3[/tex]

now put t = 3.91 s

[tex]\theta = 114.66 + 89.66[/tex]

[tex]\theta = 204.3 radian[/tex]

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