What Are Radius Vectors and Their Relationship with Velocity V?

Click For Summary
SUMMARY

The discussion clarifies the concept of radius vectors in relation to particle motion and velocity. The radius vector, denoted as \(\vec{r}\), represents the position of a particle from a defined origin at time \(t\). The velocity \(v_t\) is derived from the time derivative of the radius vector, indicating that both position and velocity vectors can change in angle relative to the origin. Specifically, while a particle may move along a circular path, its velocity vector remains tangential to the circle, demonstrating the distinction between radial and tangential motion.

PREREQUISITES
  • Understanding of vector calculus, particularly derivatives.
  • Familiarity with basic physics concepts, including motion and acceleration.
  • Knowledge of circular motion dynamics.
  • Ability to interpret vector representations in a coordinate system.
NEXT STEPS
  • Study the mathematical representation of circular motion and its implications on velocity vectors.
  • Learn about the relationship between radius vectors and angular velocity in physics.
  • Explore the concept of centripetal acceleration and its role in circular motion.
  • Investigate the application of radius vectors in different coordinate systems, such as polar coordinates.
USEFUL FOR

Students of physics, mathematicians, and anyone interested in the dynamics of particle motion and vector analysis will benefit from this discussion.

captain
Messages
163
Reaction score
0
what do radius vectors of particles really mean and how can they be at a different angle with velocity v.
 
Physics news on Phys.org
The radius vector \vec{r} is the vector from some origin to the position of the particle at some time t. Typically, \vec{r}(t) is the trajectory, so to speak of the particle, so the derivative with respect to time is the velocity: v_t = \frac{d\vec{r}}{dt}. Because the position is constantly changing, the velocity as well as the angle changes with respect to the origin.

Does that answer your question?
 
Consider yourself at the origin of a coordinate system. Any vector connecting you with an object is radial. That object may change its position, shown by a velocity vector, which is often not along the radial vector.

For instance, although motion along a circle is confined to a given radial distance out from the center, velocity is restricted to move tangent to the circle, and the acceleration enforcing circular motion orients radially toward the center!
 

Similar threads

Undergrad Angular Velocity: Vector or Not?
  • · Replies 5 ·
Replies
5
Views
2K
High School Work done when moving an object
  • · Replies 7 ·
Replies
7
Views
830
High School Is velocity ever a scalar quantity?
  • · Replies 48 ·
2
Replies
48
Views
7K
Undergrad Units of a vector in a velocity vs time graph?
  • · Replies 13 ·
Replies
13
Views
2K
Undergrad Calculation of orbital velocity -- Geometrical solution
  • · Replies 14 ·
Replies
14
Views
2K
Undergrad How can angular displacement be larger than 2pi?
  • · Replies 20 ·
Replies
20
Views
2K
Graduate Angular Velocity Vector; Relationship to Angular Momentum
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Velocity transformation between frames rotating relative to one another
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Equation of motion: choice of generalized coordinates
  • · Replies 14 ·
Replies
14
Views
2K
High School Jaan Kalda kinematics -- Radius of Curvature of a Cycloid
  • · Replies 6 ·
Replies
6
Views
2K