fisica1-youn-e-freedman-exercicios-resolvidos

10.54: a) The moment of inertia is not given, so the angular acceleration must be found
from kinematics;
2( 5.00 m)
( 0.30 m)( 2.00 s)
2θ
2s
2
α = = =
= 8.33 rad /s .
2 2
2
t rt
b) αt = ( 8.33 rad/s
2 )( 2.00 s) = 16.67 rad/s.
c) The work done by the rope on the flywheel will be the final kinetic energy;
K = W = Fs = 40 .0 N 5.0 m = 200
( )( ) J.
d)
I
2( 200 J)
( 16.67 rad/s)
2 2
K
= =
= 1.44 kg ⋅ m
ω
2 2
.
⎛ τ ⎞ 2⎛
t ⎞
10.55: a) P = τω = ταt = τ⎜
⎟t
= τ ⎜ ⎟.
⎝ I ⎠ ⎝ I ⎠
60 2
=
20.0
.0
b) From the result of part (a), the power is ( 500 W)( ) 4.50 kW.
P = = = =
2
c) τω τ 2αθ
τ 2( τ / I ) θ τ
3 / 2θ
/ I .
.00
d) From the result of part (c), the power is ( 500 W)( ) 2.6 kW.
20.00
3 / 2
6
= e) No; the
power is proportional to the time t or proportional to the square root of the angle.
10.56: a) From the right-hand rule, the direction of the torque is i ˆ × ˆj
= kˆ
, the + z
direction.
b), c)
2
d) The magnitude of the torque is F ( x − x ), which has it maximum at l 2.
The
torque at x = l 2 is F l 0
4.
0
l