To change the direction of the axis of spin the only remaining possibility is to apply a couple at right angles to the spinning axis. The axis of spin will deviate so as to direct its spin in the direction of the applied couple.
This is called Gyroscopic Precession". More precisely, "the angular momentum changes in the direction of the applied couple". Angular momentum is a measure of how fast the rotor is spinning.
With reference to the diagram, the spin axis angular momentum is the black arrow and it responds to the applied couple green arrow by changing in that direction red arrow to give a new spin axis blue , and this change in direction is called "precession" orange.
These "arrows" are called "vectors", but never mind that. To figure out the arrow relates to the direction of spin just point along the arrow and then wiggle your finger clockwise. There's an important result from all of this - you get slower precession if the spin is fast or if the couple is small.
This is because the smaller the couple, or the larger the spin angular momentum then the change in spin direction red arrow is smaller. The moon, for example, goes around the Earth at constant speed, but its' direction of travel is changing continuously due to the force of the Earth's gravity.
The axis of Earth makes a As shown in Figure 6, this axis precesses, making one complete rotation in 25, y. Figure 6. The change in angular momentum for the two shown positions is quite large, although the magnitude L is unchanged. Skip to main content. Rotational Motion and Angular Momentum. Search for:. Gyroscopic Effects: Vector Aspects of Angular Momentum Learning Objectives By the end of this section, you will be able to: Describe the right-hand rule to find the direction of angular velocity, momentum, and torque.
Explain the gyroscopic effect. Study how Earth acts like a gigantic gyroscope. Check Your Understanding Rotational kinetic energy is associated with angular momentum? Conceptual Questions 1. Integrated Concepts The axis of Earth makes a Licenses and Attributions. The proof of this is commonly found in classical mechanics textbooks. As is explained on the angular momentum page , the above equation applies for the two cases, where the local xyz axes has its origin at the center of mass G of the rigid body, or at a fixed point O on the rigid body if there is one.
In the remainder of this section, we will apply the former, so the moments, inertia terms, and angular momentum are all with respect to G. To illustrate the concept of gyroscopic stability let's say we have an axisymmetric rigid object such as a wheel spinning in space with angular velocity w , at a given instant.
Now, the magnitude of the angular momentum vector H is proportional to the magnitude of the angular velocity vector w. If there are no external moments torque acting on the object then we say that the object is experiencing torque free motion.
Therefore, the angular momentum vector has constant magnitude and direction, and angular momentum is conserved. For an axisymmetric rigid object experiencing torque free motion, the precession axis is seen from the point of view of an observer to coincide with the angular momentum vector, and this precession axis defines the average orientation of the object. This of course means that after the external impulse is applied, the object is once again experiencing torque free motion. Hence, a fast spinning axisymmetric object, experiencing torque free motion, is able to maintain its precession axis and hence average orientation with very little change, if an external impulse is applied.
Understanding the physics behind gyroscopes helps shed light on why mounting a spinning wheel powered by a motor onto a gimbal metal frame is so useful for navigation.
The spinning wheel is mounted in the gimbal so as to be free of external torque. Therefore, given its already inherent orientation stability as well as the fact that external torque is almost completely eliminated , the gyroscope experiences extremely little orientation change as a result.
This is why gyroscopes are commonly used in navigation, such as in boats and ships. They tend to remain level even if the boat or ship changes orientation either by pitching or rolling. The figure below illustrates a gyroscope-gimbal unit. The spin imparts a gyroscopic response to the aerodynamic forces acting on the projectile, which results in the projectile long axis aligning itself with the flight trajectory.
The physics involved here is a combination of gyroscopic analysis and aerodynamic force analysis due to drag and potentially the Magnus effect. This is quite complicated and will not be discussed here. However, there is a lot of literature available online on gyroscope physics, as related to projectile spin and gyroscopic stability, if one wishes to study this topic further. Next in the analysis, we will show that for an axisymmetric rigid body experiencing torque free motion, the precession axis is seen from the point of view of an observer in the inertial reference frame to coincide with the angular momentum vector, which we know is fixed in inertial ground space, with constant magnitude and direction.
Torque Free Motion Consider the figure below with local xyz axes as shown. But mathematically speaking it does not matter what axis we choose as the precession axis, since it is simply a component of rotation.
Being able to arbitrarily choose the precession axis is similar to how you can arbitrarily choose the x,y directions for a force calculation. Ultimately the answer is the same and the resultant force is not going to change. To understand this better you can read up on Euler angles which are commonly used to define the angular orientation of a body, using the concept of precession, spin, and nutation which have been used in the analysis presented here.
The next section contains some additional information that is worth mentioning. However, if this object is temporarily subjected to an external moment it will likely begin to precess as well as spin, and its new precession axis will coincide with the new angular momentum vector, which will no longer coincide with the spin axis.
To calculate the new motion of the object due to the applied external moment, you need to solve the Euler equations of motion. After the external moment has been applied, these quantities will correspond to torque free motion. In problems such as gyroscope physics analysis, solving the Euler equations of motion is necessary when moments are applied, since these equations directly account for them.
In torque free motion, the only external force acting on an object is at most gravity, which acts through the center of mass G of the object. The turning of the yellow frame is transmitted to the gyroscope wheel, and just for a moment you can see how the gyroscope wheel responds to that.
The demonstrations by professor Lewin are so vivid because he spins the wheels so fast. You definitely shouldn't try that at home. The purpose of this article is to show how to understand the behavior of the gyroscope in terms of the laws of motion. Image 6 represents the gyroscope in the demonstration by professor Lewin. To emphasize the different components I gave them contrasting colors. The swivel axis has the least freedom; the swivel axis is fixed relative to the ground. The pitch axis is always perpendicular to the ground, as it is constrained by the yellow frame.
The innermost frame, the red frame, has the most freedom. So the roll axis can point in any direction. That means roll is defined relative to the wheel. Image 7 depicts the gyroscope when it is precessing. The brown cylinder represents the weight that has been added on one end. If the gyroscope wheel would not be spinning the weight would pitch that end all the way down. In the demonstration the spin rate is much faster than the precession rate, so it's natural to think of the overall motion as a composition of two perpendicular uniform rotations: rolling and swiveling.
Image 7 shows two black arrows to depict the wheel's two component rotations. Quadrants Rather than trying to focus on a section of wheel, trying to track it, it's clarifying to look at how the parts of the wheel move through successive quadrants. Image 8 shows one such quadrant. As the wheel spins wheel mass moves through that quadrant. Motion towards the swivel axis In the quadrant shown in image 8 the mass of the wheel is moving towards the swivel axis, and so is the mass moving through the diagonally opposite quadrant.
We have that when circumnavigating mass is pulled closer to the axis of rotation the swivel axis in this case , that mass tends to pull ahead of the overall circumnavigating motion. The green arrow depicts that tendency. Motion away from the swiveling axis In the other two quadrants the mass of the wheel is moving away from the swivel axis, so the mass in those quadrants tends to lag behind the overall swiveling motion.
Pitching The four green arrows in image 7 illustrate that the effects from each of the four quadrants combine to a pitching effect. The effects from each of the four quadrants add up: they reinforce each other into a single pitching effect. In particular, this explains why a gyroscope wheel has its strong response at a 90 degrees angle. It's at 90 degrees because of the overall symmetry: the contribution of each of the four quadrants is the same, therefore the response can only be at that 90 degrees angle.
Settling into the precessing motion happens very quickly; you don't actually see it happening. It may look as if the wheel's motion has changed directly to the final precessing motion, but in fact it has gone through the above described process. Due to the fact that the gyrocopic effect is a response to motion the process of settling into precessing motion is self-adjusting: the final precessing rate is the rate of precession that keeps the wheel from pitching down further.
Picture 10 into the video shows what happens when more weight is added. The added weight increases the torque, so the wheel pitches down some more.
The motion of pitching down causes the precession to speed up. Note that professor Lewin increases the torque load gingerly.
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