# Velocity and angular acceleration

In summary, velocity is a measure of an object's speed and direction, calculated by dividing its displacement by the time it took to travel that distance. Angular acceleration is the rate of change of an object's angular velocity, and is related to linear acceleration by the radius of rotation. Tangential acceleration is parallel to an object's direction of motion, while centripetal acceleration is perpendicular and towards the center of rotation.
Is this true?

$$\vec \omega \times r = \vec v$$

That's actually meaningless.

This is true:$$\vec {\omega} \times \vec{r} = \vec {v}$$

(with respect to fixed origin)

Assuming omega is the angular velocity, r position vector, and v, the tangential velocity.

Yes, this is true. This equation represents the relationship between angular acceleration and linear velocity in a rotational motion. The cross product of the angular velocity vector and the distance vector from the axis of rotation gives the linear velocity vector. This equation is commonly used in the study of rotational motion and can be derived from the definition of angular velocity and the relationship between linear and angular speed.

## 1. What is velocity?

Velocity is a measure of how fast an object is moving in a particular direction. It is a vector quantity, meaning it has both magnitude (speed) and direction.

## 2. How is velocity calculated?

Velocity is calculated by dividing the change in an object's position (displacement) by the change in time. This means that velocity is equal to the object's displacement divided by the time it took to travel that distance.

## 3. What is angular acceleration?

Angular acceleration is the rate at which an object's angular velocity changes over time. It is a measure of how quickly an object is rotating or changing its direction of rotation.

## 4. How is angular acceleration related to linear acceleration?

Angular acceleration and linear acceleration are related through the radius of rotation. The linear acceleration of an object is equal to the angular acceleration multiplied by the radius of rotation.

## 5. What is the difference between tangential and centripetal acceleration?

Tangential acceleration is the component of linear acceleration that is parallel to the object's direction of motion. Centripetal acceleration, on the other hand, is the component of acceleration that is perpendicular to the object's direction of motion and towards the center of rotation.

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