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