fisica1-youn-e-freedman-exercicios-resolvidos

9.62:
For planetary alignment, earth must go through 60 ° more than Mars:
9.63: a) v = 60 mph = 26.82 m s
r = 12in. = 0.3048m
v
r
b) same
ω =
θ
E
= θ
M
+ 60°
wEt
= ωMt
+ 60°
60°
t =
ω − ω
w
E
E
M
360°
= and w
1yr
t =
360
1yr
60°
°
−
= 88.0rad s = 14.0 rev s = 840rpm
r = 15 in. = 0.381m
360°
1.9yr
v = rω = (0.381m)(88.0rad s) = 33.5 m s = 75 mph
c) v = 50mph = 22.35m s
M
360°
=
1.9yr
ω as in part (a) since speedometer reads same
⎛ 365d ⎞
= 0.352yr⎜
⎟ = 128 d
⎝ 1yr ⎠
r = 10 in. = 0.254 m
v
ω = = 88.0 rad s;. this is the same as for 60 mph with correct tires, so
r
speedometer read 60 mph.
2
ω
2
9.64: a) For constant angular acceleration θ = , and so a 2 .
2α
rad
= ω r = αθr
b) Denoting the angle that the acceleration vector makes with the radial direction as β ,
and using Equations (9.14) and (9.15),
atan
α r α r 1
tan β = = = = ,
2
a ω r 2 αθ r 2θ
so
1 1
θ = = =
2 tan β 2 tan 36.9°
0.666 rad.
rad