# Gyroscope- Angular Momentum and Torque

• Fizzios
In summary, the conversation discusses the concepts of angular momentum and torque in relation to gyroscopes. The speaker is confused about why angular momentum is measured from the center of the spinning disk while torque is measured from the origin. It is explained that for an object with no net linear momentum, the choice of reference point does not affect the angular momentum. The discussion also mentions the use of a reference point at the center of mass to compute torque. Ultimately, it is clarified that the change in angular momentum can be measured anywhere along the axis of the gyroscope and that in a gravity-free environment, a torque couple may be needed to produce precession motion.
Fizzios
I was reading on gyroscopes, and everything seemed to make sense: the spin angular momentum along the axis of the gyroscope changes due to the torque by gravity, causing precession. However, I can't understand why we are measuring angular momentum (the spin of the gyroscope) from the center of the spinning disk, but the torque from the origin (pivot point). Aren't we supposed to measure torque and angular momentum about the same point to use the relation Torque = dL/dt?

Some clarification would be much appreciated!

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For an object with no net linear momentum (e.g. a gyroscope spinning more or less in place), its angular momentum will not depend on what reference point you choose as the origin.

For a torque being applied by a "couple" (a pair of equal but opposite forces that act on parallel lines rather than on the same line, e.g. N and W), it does not matter what reference point you use to compute the net torque.

Or you can avoid the problem and compute the torque produced from the upward force N using a reference point at the center of mass of the gyroscope.

Thanks, I see. So it would be safe to say that you get the same change in angular momentum measured anywhere along the axis of the gyroscope?

Also, hypothetically, in a gravity-free environment, if someone were to push a spinning gyroscope at the pivot (acting like the normal force), would it produce the same precession motion? Or is a torque couple needed?

Yes, the angular momentum for an object spinning around an axis is the same no matter where on the axis you choose to measure it from.

In a gravity-free environment the gyroscope will be accelerating in the direction of the net force. But you can choose to analyze the system from an accelerating frame in which the center of mass is motionless (like in an elevator that is accelerating upward). In this frame there is a downward inertial force that acts just like gravity. So you can have a force couple if you want one.

I can understand your confusion about measuring angular momentum and torque from different points. However, in the case of a gyroscope, it is important to differentiate between the two.

Angular momentum, also known as rotational momentum, is a vector quantity that measures the amount of rotational motion an object has around a specific axis. In the case of a gyroscope, the axis of rotation is the center of the spinning disk. Therefore, we measure the angular momentum of the gyroscope from its center.

On the other hand, torque is also a vector quantity that measures the force applied to an object to cause it to rotate around an axis. In the case of a gyroscope, the torque is acting at the pivot point, which is typically at the base of the gyroscope. This torque is what causes the precession of the gyroscope.

So, while it may seem counterintuitive to measure angular momentum from the center and torque from the pivot point, it is necessary to differentiate between the two in order to fully understand the dynamics of a gyroscope. The relation Torque = dL/dt still holds true, as the torque is causing a change in the angular momentum of the gyroscope.

I hope this explanation helps to clarify any confusion you may have had about measuring angular momentum and torque in the context of a gyroscope. Keep exploring and learning about this fascinating device!

## 1. What is a gyroscope?

A gyroscope is a device that consists of a spinning wheel or disc that is mounted on an axis. It is used to measure and maintain orientation and angular momentum. Gyroscopes are commonly used in navigation systems, robotics, and other applications where precise orientation is necessary.

## 2. How does a gyroscope work?

A gyroscope works by utilizing the principles of conservation of angular momentum and torque. When the gyroscope spins, it creates a stable platform that resists any external forces that try to change its orientation. This allows it to accurately measure and maintain its position in space.

## 3. What is angular momentum?

Angular momentum is a measure of an object's tendency to resist changes in its rotational motion. It is calculated by multiplying an object's moment of inertia by its angular velocity. In the case of a gyroscope, the spinning disc or wheel creates angular momentum that helps it maintain its orientation.

## 4. What is torque?

Torque is a measure of the force that causes an object to rotate around an axis. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation. In the case of a gyroscope, torque is produced by the spinning wheel or disc, which helps it maintain its orientation.

## 5. What are the practical applications of gyroscopes?

Gyroscopes have a wide range of practical applications, including navigation systems, stabilizing devices for vehicles and other moving objects, and in robotics and spacecraft. They are also used in smartphones and other electronic devices for motion sensing and orientation tracking.

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