fisica1-youn-e-freedman-exercicios-resolvidos

9.70: a) The angular acceleration will be zero when the speed is a maximum, which is at
the bottom of the circle. The speed, from energy considerations, is
v = 2gh
= 2gR(1
− cosβ ), where β is the angle from the vertical at release, and
2
v 2g
2(9.80 m s )
ω = = (1 − cosβ
) =
(1 − cos 36.9°
) = 1.25 rad s.
R R
(2.50 m)
b) α will again be 0 when the meatball again passes through the lowest point.
a is directed toward the center, and a
2
= ω R,
a
2
= (1.25 rad s ) (2.50 m) 3.93 m
c)
rad
rad rad
=
2
d) a = ω R = (2g
R)(1
− cos β)
R = (2g)(1
− cos β),
independent of R.
rad
2
9.71: a) (60.0 rev s)(2π
rad rev)(0.45× 10
− m) = 1.696 m s.
v 1.696 m s
b) ω = 84.8 rad s.
=
2
=
r
−
2.00 × 10 m
9.72: The second pulley, with half the diameter of the first, must have twice the angular
velocity, and this is the angular velocity of the saw blade.
⎛ π rad s ⎞ ⎛ 0.208 m ⎞
a) ( 2(3450 rev min)) ⎜ ⎟ ⎜ ⎟ = 75.1m s.
⎝ 30 rev min ⎠ ⎝ 2 ⎠
⎛
2
⎛ π rad s ⎞⎞
⎛ 0.208 m ⎞
4 2
b) a
rad
= ω r = ⎜2(3450 rev min)
⎟
⎜ ⎟ ⎜ ⎟ = 5.43×
10 m s ,
30 rev min
⎝
⎝ ⎠⎠
⎝ 2 ⎠
so the force holding sawdust on the blade would have to be about 5500 times as strong as
gravity.
2