In a judo foot-sweep move, you sweep your opponent's left foot out from under him while pulling on his gi (uniform) toward that side. As a result, your opponent rotates around his right foot and onto the mat. Figure 10-44 shows a simplified diagram of your opponent as you face him, with his left foot swept out. The rotational axis is through point O. The gravitational force F g → on him effectively acts at his center of mass, which is a horizontal distance d = 28 cm from point O . His mass is 70 kg, and his rotational inertia about point O is 65 kg · m 2 . What is the magnitude of his initial angular acceleration about point O if your pull F a → on his gi is (a) negligible and (b) horizontal with a magnitude of 300 N and applied at height h = l.4m? Figure 10-44 Problem 54.
In a judo foot-sweep move, you sweep your opponent's left foot out from under him while pulling on his gi (uniform) toward that side. As a result, your opponent rotates around his right foot and onto the mat. Figure 10-44 shows a simplified diagram of your opponent as you face him, with his left foot swept out. The rotational axis is through point O. The gravitational force F g → on him effectively acts at his center of mass, which is a horizontal distance d = 28 cm from point O . His mass is 70 kg, and his rotational inertia about point O is 65 kg · m 2 . What is the magnitude of his initial angular acceleration about point O if your pull F a → on his gi is (a) negligible and (b) horizontal with a magnitude of 300 N and applied at height h = l.4m? Figure 10-44 Problem 54.
Solution Summary: The author explains how angular acceleration for both cases can be found. The rotational axis is at point O, and the gravitational force acts along the player's center of mass.
In a judo foot-sweep move, you sweep your opponent's left foot out from under him while pulling on his gi (uniform) toward that side. As a result, your opponent rotates around his right foot and onto the mat. Figure 10-44 shows a simplified diagram of your opponent as you face him, with his left foot swept out. The rotational axis is through point O. The gravitational force
F
g
→
on him effectively acts at his center of mass, which is a horizontal distance d = 28 cm from point O. His mass is 70 kg, and his rotational inertia about point O is 65 kg · m2. What is the magnitude of his initial angular acceleration about point O if your pull
F
a
→
on his gi is (a) negligible and (b) horizontal with a magnitude of 300 N and applied at height h = l.4m?
Figure 10-44 Problem 54.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
In a judo foot-sweep move, you sweep your opponent's left foot out from under him while pulling on his gi (uniform) toward that side.
As a result, your opponent rotates around his right foot and onto the mat. The figure shows a simplified diagram of your opponent as
you face him, with his left foot swept out. The rotational axis is through point O. The gravitational force Fg on him effectively acts at
his center of mass, which is a horizontal distance d = 21 cm from point O. His mass is 73 kg, and his rotational inertia about point O is 65
kg.m². What is the magnitude of his initial angular acceleration about point O if your pull Fa on his gi is (a) negligible and (b)
horizontal with a magnitude of 300 N and applied at height h = 1.4 m? Assume free-fall acceleration to be equal to 9.81 m/s².
(a) Number i
Units
(b) Number
Units
com
F
>
In a judo foot-sweep move, you sweep your opponent's left foot out from under him while pulling on his gi (uniform) toward that side.
As a result, your opponent rotates around his right foot and onto the mat. The figure shows a simplified diagram of your opponent as
you face him, with his left foot swept out. The rotational axis is through point O. The gravitational force F & on him effectively acts at
his center of mass, which is a horizontal distance d = 23 cm from point O. His mass is 71 kg, and his rotational inertia about point O is 65
а
g
kg.m². What is the magnitude of his initial angular acceleration about point O if your pull Ễ, on his gi is (a) negligible and (b)
horizontal with a magnitude of 300 N and applied at height h = 1.4 m? Assume free-fall acceleration to be equal to 9.81 m/s².
(a) Number
Units
(b) Number
Units
com
h
Heading straight toward the summit of Pikes Peak, an airplane of mass 17000 kg flies over the plains of Kansas at nearly constant altitude of 4.30 km with a constant velocity of 160 m/s west.
(a) What is the airplane's vector angular momentum relative to a wheat farmer on the ground directly below the airplane?
J kg-m²/s
(b) Does this value change as the airplane continues its motion along a straight line?
O yes
O no
(c) What is its angular momentum relative to the summit of Pikes Peak?
|kg-m²/s
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