page_title: Precession
section_title: Torque-induced
hierarchical_section_title: Precession / Torque-induced
caption_attribution_description: Deutsch: Kreisel in kardanischer Aufhängung. Beschriftet für Erklärung der Kreiselmomente als direkte Folge von Coriolis-Kräften. Kann Präzession und Selbstfindung der Nordrichtung von Kreiselkompassen verdeutlichen. English: Turnable gimbal holding gyro. Labelled to explain coriolisforces as reason of momentum generated by applying a momentum to the gyro. Suitable to explain precession as well as self-actuating orientation to north of a gyrocompass. From inside to outside there are three axes of rotation: the hub of the wheel, the gimbal axis and the vertical pivot. To distinguish between the two horizontal axes, rotation around the wheel hub will be called 'rolling,' and rotation around the gimbal axis will be called 'pitching.' First, imagine that the device is rotating around the pivot axis. Then some rotation around the wheelhub is added. Imagine the gimbal axis to be locked, so that the wheel cannot pitch. The gimbal axis has sensors, that measure whether there is a torque around the gimbal axis. The device is spinning around the vertical axis, and then some roll is added. In the picture, a section of the wheel has been named 'dm1'. When the rolling starts, section dm1 is at the perimeter of the spinning motion. Section dm1 has a lot of velocity and as it is forced closer to the center of rotation, it tends to move in the direction of the top-left arrow in the diagram (shown at 45o in the direction of rolling). Section dm2 of the wheel starts out at the center of rotation, and thus initially has zero velocity. A force would be required to increase section dm2's velocity to the velocity at the perimeter of the pivot axis' plane. If that force is not provided then section dm2's inertia will make it move in the direction of the top-right arrow. Note that both arrows point in the same direction. The same reasoning applies for the bottom half of the wheel, but there the arrows point in the opposite direction to that of the top arrows. Combined over the entire wheel, there is a torque around the gimbal axis when some rolling is added to rotation around a vertical axis. It is important to note that the torque arises without any delay; the response is instantaneous.
context_page_description: Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.
  In astronomy, precession refers to any of several slow changes in an astronomical body's rotational or orbital parameters. An important example is the steady change in the orientation of the axis of rotation of the Earth, known as the precession of the equinoxes.
context_section_description: Torque-induced precession (gyroscopic precession) is the phenomenon in which the axis of a spinning object (e.g., a gyroscope) describes a cone in space when an external torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude of the external torque are constant, the spin axis will move at right angles to the direction that would intuitively result from the external torque. In the case of a toy top, its weight is acting downwards from its center of mass and the normal force (reaction) of the ground is pushing up on it at the point of contact with the support. These two opposite forces produce a torque which causes the top to precess.
  The device depicted on the right (or above on mobile devices) is gimbal mounted. From inside to outside there are three axes of rotation: the hub of the wheel, the gimbal axis, and the vertical pivot.
  To distinguish between the two horizontal axes, rotation around the wheel hub will be called spinning, and rotation around the gimbal axis will be called pitching.  Rotation around the vertical pivot axis is called rotation.
  First, imagine that the entire device is rotating around the (vertical) pivot axis. Then, spinning of the wheel (around the wheelhub) is added. Imagine the gimbal axis to be locked, so that the wheel cannot pitch. The gimbal axis has sensors, that measure whether there is a torque around the gimbal axis.
  In the picture, a section of the wheel has been named dm₁. At the depicted moment in time, section dm₁ is at the perimeter of the rotating motion around the (vertical) pivot axis. Section dm₁, therefore, has a lot of angular rotating velocity with respect to the rotation around the pivot axis, and as dm₁ is forced closer to the pivot axis of the rotation (by the wheel spinning further), because of the Coriolis effect, with respect to the vertical pivot axis, dm₁ tends to move in the direction of the top-left arrow in the diagram (shown at 45°) in the direction of rotation around the pivot axis.  Section dm₂ of the wheel is moving away from the pivot axis, and so a force (again, a Coriolis force) acts in the same direction as in the case of dm₁. Note that both arrows point in the same direction.
  The same reasoning applies for the bottom half of the wheel, but there the arrows point in the opposite direction to that of the top arrows. Combined over the entire wheel, there is a torque around the gimbal axis when some spinning is added to rotation around a vertical axis.
  It is important to note that the torque around the gimbal axis arises without any delay; the response is instantaneous.
  In the discussion above, the setup was kept unchanging by preventing pitching around the gimbal axis. In the case of a spinning toy top, when the spinning top starts tilting, gravity exerts a torque. However, instead of rolling over, the spinning top just pitches a little. This pitching motion reorients the spinning top with respect to the torque that is being exerted. The result is that the torque exerted by gravity – via the pitching motion – elicits gyroscopic precession (which in turn yields a counter torque against the gravity torque) rather than causing the spinning top to fall to its side.
  Precession or gyroscopic considerations have an effect on bicycle performance at high speed. Precession is also the mechanism behind gyrocompasses.
caption: The response of a rotating system to an applied torque. When the device swivels, and some roll is added, the wheel tends to pitch.
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