Question

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.

Answer 1

Ф = 239.73 rad

Step-by-step 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