Adisk rotates at constant angular acceleration, from angular position θ1 = 16.0 rad to angular position θ2 = 76.0 rad in 5.30 s. its angular velocity at θ2 is 11.0 rad/s.

(a) what was its angular velocity at θ1?
(b) what is the angular acceleration?
(c) at what angular position was the disk initially at rest?

(a) the angular velocity at θ1 is 11.64 rad/s

(b) the angular acceleration is 0.12 rad/

(c) the angular position was the disk initially at rest is - 428.27 rad

Explanation:

Given information :

θ1 = 16 rad

θ2 = 76 rad

ω2 = 11 rad/s

t = 5.3 s

(a) The angular velocity at θ1

First, we use the angular motion equation for constant acceleration

Δθ = (ω1+ω2)t/2

θ2 - θ1 = (ω1+ω2)t/2

ω1 + ω2 = 2 (θ2 - θ1) / t

ω1 = (2 (θ2 - θ1) / t ) - ω2

     = (2 (76-16) / 5.3) - 11

     = 11.64 rad/s

(b) the angular acceleration

ω2 = ω1 + α t

α t = ω2 - ω1

α = (ω2 - ω1)/t

  = (11.64 - 11) / 5.3

  = 0.12 rad/

(c) the angular position was the disk initially at rest, θ0

at rest ω0 = 0

ω2^2 = ω01  t + 2 α Δθ

2 α Δθ = ω2^2

θ2 - θ0 = ω2^2  /  2 α

θ0 = θ2 -  (ω2^2) / 2 α

  = 76 - (/ 2 x 0.12

  = 76 - 504.16

  = - 428.27 rad