Biomedical Engineering Reference
In-Depth Information
Torque of the reaction force:
M
FR
¼
(600 N)(0.15 m)
¼
90 N m.
Angular impulse due to this torque:
I
A
¼
45 N m s.
This impulse corresponds to the angular momentum introduced:
L
(90 N m)(0.5 s)
¼
45 kg m
2
/s.
¼
mk
2
, that is, 45 kg m
2
/s
(60 kg)(0.45 m)
2
L
¼
I
ω ¼
ω
¼
ω
.
45 kg m
2
=
s
ω ¼
2
¼
3
:
7 rad
=
s
; ω ¼
3
:
7 rad
=
s
:
ð
60 kg
Þ
ð
0
:
45m
Þ
Exercise 4.5
Consider the rotation of a body with 8 kg mass with the radius of
gyration
k
3 rad/s. Find the moment of inertia
and the angular momentum. Repeat the exercise in case each of the quantities is
doubled, changing each time only one of the variables.
¼
0.2 m and angular velocity
ω ¼
Exercise 4.6
In the table of Exercise 4.6 are given the moments of inertia about the
main longitudinal axis for a dancer in two different moments of evolution and
respective angular velocities. Obtain the angular momentum in each situation and
try to justify the maneuver performed by the dancer.
Table of Exercise 4.6
I
C.G.
(kg m
2
)
Evolution
ω
(rad/s)
A
3.0
20.0
B
5.0
12.0
Exercise 4.7
The arm, with 3.5 kg mass, of a volleyball player moves with an
angular velocity of 18 rad/s about his shoulder, during the spike. Considering that
the moment of inertia of the extended arm is 0.40 kg m
2
, determine the following:
(a) The radius of gyration of the arm
(b) The angular momentum of the arm during the spike
Exercise 4.8
A diver of 70 kg mass jumps from the springboard, facing the swim-
ming pool. At the moment of the jump, he assumes such a posture that the radius of
gyration of his body is 0.50 m, about the main transverse axis. He leaves the
springboard with an angular velocity of 2 rad/s. Determine the magnitude of external
torque that has introduced the angular momentum on the diver, knowing that the force
of the reaction that gave origin to this angular momentum had a duration of 0.4 s.
4.7 Answers to Exercises
0.145 kg m
2
; (b)
k
b
¼
Exercise 4.1
(a)
k
a
¼
22.0 cm and
I
a
¼
2.1 cm and
0.00135 kg m
2
.
I
b
¼
2.023 kg m
2
. With the arms opened, the degree of difficulty is
twice that when a person is with both arms near the body and along the body.
Exercise 4.2 I
¼
