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5.9. Gyroscope. Gyroscopic effect

Lecture



A gyroscope (or a top) is called a massive symmetric body, rotating at high speed around the axis of symmetry (Fig.5.5).


  5.9.  Gyroscope.  Gyroscopic effect

The moment of the momentum of the gyroscope coincides with its axis of rotation. In order to change the direction in space of the axis of the gyroscope, i.e. vector direction   5.9.  Gyroscope.  Gyroscopic effect necessary in accordance with the basic equation of the dynamics of rotational motion   5.9.  Gyroscope.  Gyroscopic effect act upon it with a moment of external forces   5.9.  Gyroscope.  Gyroscopic effect . Let it be a couple of forces   5.9.  Gyroscope.  Gyroscopic effect creating torque about the axis   5.9.  Gyroscope.  Gyroscopic effect lying in the plane of the drawing perpendicular to the axis of the OO (rotation around   5.9.  Gyroscope.  Gyroscopic effect ). In this case, there is the following phenomenon, called the gyroscopic effect: under the action of a pair of forces, which, it would seem, should have caused the rotation of the axis of the gyroscope OO around the axis   5.9.  Gyroscope.  Gyroscopic effect the axis of the gyro rotates around a straight line   5.9.  Gyroscope.  Gyroscopic effect perpendicular to these axes (i.e., OO and   5.9.  Gyroscope.  Gyroscopic effect ). At first glance, the gyroscope’s “unnatural” behavior turns out to be completely consistent with the laws of the dynamics of the rotational motion, i.e ultimately, Newton's laws. Consider the behavior of the gyroscope under the action of the moment of force   5.9.  Gyroscope.  Gyroscopic effect acting along the axis   5.9.  Gyroscope.  Gyroscopic effect . During   5.9.  Gyroscope.  Gyroscopic effect gyro moment of momentum   5.9.  Gyroscope.  Gyroscopic effect increment   5.9.  Gyroscope.  Gyroscopic effect which has the same direction as   5.9.  Gyroscope.  Gyroscopic effect . The moment of the momentum of the gyroscope after time   5.9.  Gyroscope.  Gyroscopic effect will be equal to the resultant   5.9.  Gyroscope.  Gyroscopic effect lying in the plane of the drawing. Vector direction   5.9.  Gyroscope.  Gyroscopic effect coincides with the new direction of the axis of rotation of the gyroscope. Thus, the axis of the gyro will rotate around the axis   5.9.  Gyroscope.  Gyroscopic effect (perpendicular to the plane of the drawing), and so that the angle between the vectors   5.9.  Gyroscope.  Gyroscopic effect and   5.9.  Gyroscope.  Gyroscopic effect decreases: If a gyroscope acts for a long time with a constant in the direction of the moment of external forces, then the axis of the gyroscope is finally set so that the axis and direction of proper rotation coincide with the axis and direction of rotation under the action of external forces (vector   5.9.  Gyroscope.  Gyroscopic effect , coincides in direction with the vector   5.9.  Gyroscope.  Gyroscopic effect ).


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Physical foundations of mechanics

Terms: Physical foundations of mechanics