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 long jump, an athlete leaves the ground with an initial angular momentum that tends to rotate her body forward, threatening to ruin her landing.To counter this tendency, she rotates her outstretched arms to “take up” the angular momentum (Fig. 11- 18). In 0.700 s, one arm sweeps through 0.500 rev and the other arm sweeps through 1.000 rev.Treat each arm as a thin rod of mass 4.0 kg and length 0.60 m, rotating around one end. In the athlete’s reference frame, what is the magnitude of the total angular momentum of the arms around the common rotation axis through the shoulders?
An irregular flat object of mass m has a moment of inertia I, when nailed loosely to a vertical wall. Its center of mass is a distance d from where it is nailed to the wall, and the object is rotated such that the line from the nail to the center of mass makes an angle (theta) relative to the horizontal. When released, what wil be the object's initial angular acceleration?
A uniform 3.7-kg cylinder can rotate about an axis through its center at O. The forces applied are: F1 = 4.5 N, F2 = 7.1 N, F3 = 5.8 N, and F4 = 3.8 N. Also, R1 = 11.1 cm and R3 = 6.2 cm. Find the magnitude and direction (+: counterclockwise; -: clockwise) of the angular acceleration of the cylinder.
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