# Finding the derivative of the radial vector r

• zachdr1
In summary, the radial vector r is a vector that represents the distance and direction from a fixed point to a given point in space. Finding its derivative allows us to determine the rate of change of this distance and direction, which is useful in various fields. The formula for finding the derivative is d/dt (r) = (dr/dt) + (r x dθ/dt), where r is the distance, θ is the angle, and t is time. The derivative is related to velocity as it represents the magnitude of the velocity vector, and to acceleration as the second derivative represents the rate of change of velocity. It can be negative, indicating a decrease in distance and a clockwise change in direction.
zachdr1

## Homework Statement

How do you find the derivative of the radial vector r

## Homework Equations

r [/B]= ru'_r + ru_r

$$r = \frac{dr}{dt}u_r + r\frac{du_r}{dt}$$

can't get latex to work either

## The Attempt at a Solution

[/B]
If r is the magnitude of r, how would you find the derivative of it? Wouldn't it be constant?

Last edited:
zachdr1 said:
If r is the magnitude of r, how would you find the derivative of it? Wouldn't it be constant?
It would be constant only if the object is at rest or moving in a circle.

## 1. What is the definition of the radial vector r?

The radial vector r is a vector that represents the distance and direction from a fixed point, usually the origin, to a given point in space.

## 2. Why is finding the derivative of the radial vector r important?

Finding the derivative of the radial vector r allows us to determine the rate of change of the distance and direction from the fixed point to a given point. This is useful in many fields such as physics, engineering, and mathematics.

## 3. What is the formula for finding the derivative of the radial vector r?

The formula for finding the derivative of the radial vector r is d/dt (r) = (dr/dt) + (r x dθ/dt), where r is the distance, θ is the angle, and t is time.

## 4. How is the derivative of the radial vector r related to velocity and acceleration?

The derivative of the radial vector r is related to velocity because it represents the rate of change of the distance from the fixed point, which is also the magnitude of the velocity vector. It is related to acceleration because the second derivative of the radial vector r represents the rate of change of the velocity, which is acceleration.

## 5. Can the derivative of the radial vector r be negative?

Yes, the derivative of the radial vector r can be negative. This would indicate that the distance from the fixed point is decreasing with respect to time, and the direction is changing in a clockwise direction.

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