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

$\alpha = 15 + 9t$

$\frac{dw}{dt} = 15 + 9t$

integrating both sides

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

again we can write

$\frac{d\theta}{dt} = 15t + 4.5 t^2$

again integrating both sides

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

now put t = 3.91 s

$\theta = 114.66 + 89.66$

$\theta = 204.3 radian$