p11_012.pdf

12. We assume the sense of rotation is positive, which (since it starts from rest) means all quantities (angular

displacements, accelerations, etc.) are positive-valued.

(a) The angular acceleration satisﬁes Eq. 11-13:

2 α (5 . 0s) 2

⇒

α =2 . 0rad / s 2

(b) The average angular velocity is given by Eq. 11-5:

ω avg = ∆ θ

∆ t = 25 rad

5 . 0s

=5 . 0rad / s .

ω = 2 . 0rad / s 2 (5 . 0s)=10rad / s .

(d) According to Eq. 11-13, the angular displacement at t =10sis

2 αt 2 =0+ 1

2 (2 . 0)(10) 2 = 100 rad .

Thus, the displacement between t =5sand t =10sis∆ θ = 100

−

25 = 75 rad.

25 rad = 1

θ = ω 0 + 1