Calculating Relative Speed in Circular Motion: Two Cyclists on a Track

Click For Summary

Discussion Overview

The discussion revolves around calculating the relative speed of two cyclists, A and B, moving on a circular track. Cyclist A travels along the circumference while Cyclist B travels through the diameter. The focus is on understanding the relationship between their velocities, the angles involved, and the implications of their motion in circular motion dynamics.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant introduces the problem of finding the speed of Cyclist A with respect to Cyclist B, given their constant speed, radius, and angles.
  • Another participant suggests that the relative velocity depends on the angles between the velocity vectors of A and B, indicating that A initially moves away from B until reaching a quarter arc.
  • It is noted that Cyclist B's velocity vector is constant and directed along the x-axis, while Cyclist A's velocity vector is tangential to the circle.
  • A participant mentions that the relative speed can be calculated as the magnitude of the difference between the velocity vectors of A and B.
  • There is a clarification regarding a formula where one participant questions the notation used for time, leading to a correction of a previous statement about the relationship between distance and speed.

Areas of Agreement / Disagreement

Participants appear to agree on the basic setup of the problem and the need to consider angles and velocity vectors, but there is no consensus on the specific calculations or the implications of the angles involved.

Contextual Notes

The discussion includes assumptions about the constant speed and the nature of circular motion, but does not resolve the mathematical steps needed to derive the relative speed explicitly.

Who May Find This Useful

This discussion may be useful for students or individuals interested in understanding relative motion in circular dynamics, particularly in the context of physics problems involving multiple moving objects.

Trooko
Messages
8
Reaction score
0
  • Two cyclists( A, B) traveling with the same constant speed, v,
  • in a circular track.
  • They start at the same point on the circle.
  • cyclist B travel through the diameter of the circle, assume the x-axis on a xy
  • Cyclist A travel on the circumference of the circle

  • Find speed of A with respect to B.

Given: the constant speed, radius, angle between A and the x-axis through the centre, angle between A and B.

am I suppose to do something with the acceleration (normal/centripedal) and the two angles given.

thank you
 
Physics news on Phys.org
Trooko said:
Given: the constant speed, radius, angle between A and the x-axis through the centre, angle between A and B.

am I suppose to do something with the acceleration (normal/centripedal) and the two angles given.
It has to do with the velocity of each, and the velocity of A with respect to B is dependent on the angles between the velocity vectors.

When A and B start, A is moving away from B, and only starts moving toward B after A passes the quarter arc.

At time t = v/D = v/2R, B moves outside A's circular trajectory.

[itex]\vec_B[/itex] is always v[itex]\,\hat{x}[/itex], whereas

[itex]\vec_A[/itex] is always v[tex]\,\hat{\theta}[/tex] where [tex]\hat{\theta}[/tex] is the unit vector in the azimuthal direction (tangent to circumference of circle). As xB gets very large, the angle between A and B gets very small.

The 'speed' would be the magnitude of the velocity vector given by [itex]\vec_A[/itex] - [itex]\vec_B[/itex]
 
Thanks for the reply. It really does look a lot simpler now.

But when you wrote t= V/D, did you mean t = D/V?
 
Trooko said:
Thanks for the reply. It really does look a lot simpler now.

But when you wrote t= V/D, did you mean t = D/V?
Yes, t = D/V. My mistake.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 37 ·
2
Replies
37
Views
5K
  • · Replies 4 ·
Replies
4
Views
1K
Replies
6
Views
4K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 1 ·
Replies
1
Views
5K