A bar on a hinge starts from rest and rotates with an angular acceleration α = 12 + 5t, where α is in rad/s2 and t is in seconds. Determine the angle in radians through which the bar turns in the first 4.88 s.

Ф = 239.73 rad

Explanation:

α = 12 + 15*t

W = ∫α*dt

= ∫ (12 + 5*t) * dt

= 12*t + 2.5*t^2

then:

Ф = ∫W*dt

= ∫ (12*t + 2.5*t^2) dt

= 6*t^2 + 5/6*t^3

therefore the angle at t = 4.88s is:

Ф = 6 * (4.88) ^2 + 5/6 * (4.88) ^3

= 239.73 rad