# Angular vel. and mom.-origins vs. axes

• TomServo
In summary, Angular velocity and angular momentum are both vectors, but angular velocity is not measured with respect to an axis. Angular momentum, on the other hand, is measured with respect to an origin or point. In cases where only the magnitude of angular momentum changes, we can assume that it lies along the axis without explicitly stating it.
TomServo
Angular vel. and mom.--origins vs. axes

This is a conceptual question.

Angular velocity is measured with respect to an axis, correct?

Yet angular momentum is measured with respect to an origin, i.e. a point, correct?

For angular momentum problems where only the magnitude of angular momentum changes, it seemed like we were calculating L with respect to an axis, but that was not correct, strictly speaking, right?

Hi TomServo!
TomServo said:
This is a conceptual question.

Angular velocity is measured with respect to an axis, correct?

Yet angular momentum is measured with respect to an origin, i.e. a point, correct?

Angular velocity and angular momentum are both vectors (strictly, psuedovectors)

Angular momentum is measured wrt a point

Angular velocity isn't
For angular momentum problems where only the magnitude of angular momentum changes, it seemed like we were calculating L with respect to an axis, but that was not correct, strictly speaking, right?

Right! In that case, we are assuming (correctly) that the angular momentum lies along that axis, without bothering to say so!

## 1. What is angular velocity and how does it relate to the origin and axes?

Angular velocity is a measure of the rate of change of angular displacement of an object. It is defined as the change in angular position divided by the change in time. The origin and axes refer to the point and direction from which the angle is measured. Angular velocity is dependent on the choice of origin and axes.

## 2. How are angular velocity and momentum related?

Angular velocity and momentum are related through the concept of angular momentum, which is defined as the product of the moment of inertia and angular velocity. This means that an object with a large moment of inertia will have a lower angular velocity for the same amount of angular momentum, and vice versa.

## 3. Can the choice of origin and axes affect the measurement of angular velocity and momentum?

Yes, the choice of origin and axes can greatly affect the measurement of angular velocity and momentum. This is because these quantities are dependent on the reference point and direction chosen, and can change significantly when the origin and axes are altered.

## 4. How does the right-hand rule relate to angular velocity and momentum?

The right-hand rule is a rule used to determine the direction of angular velocity and momentum. According to this rule, if the fingers of your right hand curl in the direction of rotation, then the thumb points in the direction of the angular velocity or momentum vector.

## 5. How can angular velocity and momentum be calculated?

Angular velocity can be calculated by dividing the change in angular position by the change in time. Momentum, on the other hand, can be calculated by multiplying the moment of inertia by the angular velocity. Both of these quantities can also be calculated using the equations of motion for rotational motion.

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