fisica1-youn-e-freedman-exercicios-resolvidos

dθ
2
2
3 2
9.65: a) ω z
= = 2γt
− 3βt
= (6.40 rad s ) t − (1.50 rad s ) t .
dt
dwz
2
3
b) αz
= = 2γ
− 6β t = (6.40 rad/s ) − (3.00 rad/s ) t.
dt
c) An extreme of angular velocity occurs when α = 0, which occurs at
γ
2
3.20 rad/s
t = 2.13 s, and at this time
=
3 β
3
=
1.50 rad/s
ω
2 2
2 2 (3.20 rad/s )
= ( 2γ)(
γ /3β)
− (3β)(
γ /3β)
= γ /3β
=
3
3(0.500 rad/s )
z
z
=
6.83rad/s.
9.66: a) By successively integrating Equations (9.5) and (9.3),
β 2
2
3 2
ωz
= γt − t = (1.80 rad/s ) t − (0.125 rad/s ) t ,
2
γ 2 β 3
2 2
3 3
θ = t − t = (0.90 rad/s ) t − (0.042 rad/s ) t .
2 6
b) The maximum positive angular velocity occurs when α
z
= 0, t = γ , the angular
β
velocity at this time is
2
2
2 2
⎛ γ ⎞ β ⎛ γ ⎞ 1 γ 1 (1.80 rad/s )
ω z
= γ⎜
⎟ − ⎜ ⎟ = =
= 6.48 rad/s.
3
⎝ β ⎠ 2 ⎝ β ⎠ 2 β 2 (0.25 rad/s )
2γ
The maximum angular displacement occurs when ω
z
= 0, at time t = (t = 0 is an
β
inflection point, and θ(0)
is not a maximum) and the angular displacement at this time is
2
3
3
2 3
γ ⎛ 2γ
⎞ β ⎛ 2γ
⎞ 2 γ 2 (1.80 rad/s )
θ = ⎜ ⎟ − ⎜ ⎟ = = = 62.2 rad.
2
3 2
2 ⎝ β ⎠ 6 ⎝ β ⎠ 3 β 3 (0.25 rad/s )
9.67: a) The scale factor is 20.0, so the actual speed of the car would be 35 km h = 9.72 m
2
2K
b) (1 2) mv 8.51J. c) ω =
=
I
= 652 rad s.