Question

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.

Answer 1

As we know that angular acceleration is given by

`\alpha = 15 + 9t`

`(dw)/(dt) = 15 + 9t`

integrating both sides

`w - 0 = 15t + 4.5 t^2`

again we can write

`(d\theta)/(dt) = 15t + 4.5 t^2`

again integrating both sides

`\theta = 7.5t^2 + 1.5t^3`

now put t = 3.91 s

`\theta = 114.66 + 89.66`

`\theta = 204.3 radian`