How many constraints are there when the particle is moving in a plane

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Discussion Overview

The discussion revolves around the number of constraints on a particle moving in a plane versus in three-dimensional space. Participants explore the relationship between spatial quantities and constraints, as well as the equations needed to define a plane in three dimensions.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions how many spatial quantities are needed to determine a particle's position over time, suggesting that three are needed in three dimensions and two in a plane.
  • Another participant proposes that the number of equations relating spatial quantities indicates the constraints on the system.
  • There is a suggestion that if a plane exists within a three-dimensional space, it imposes constraints on the particle's motion.
  • Some participants propose that two constraints may apply when considering motion in a plane within three-dimensional space.
  • Another participant argues that three equations are necessary to specify a plane, while another counters that only one equation is needed.
  • There is a discussion about the form of the equation that defines a plane, with a participant providing the equation ax + by + cz = 0.

Areas of Agreement / Disagreement

Participants express differing views on the number of constraints and equations needed to define a plane, leading to unresolved disagreements regarding the specifics of constraints in both two and three dimensions.

Contextual Notes

Participants have not reached a consensus on the number of constraints or the equations required to define a plane, and there are varying interpretations of how to relate spatial quantities to constraints.

roshan2004
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How many constraints are there when the particle is moving in a plane and on three dimensional space and what are they?
 
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Ask yourself:

1. How many spatial quantities must be specified in order to uniquely determine the particle's position as a function of time?

2. How many equations exist that relate those spatial quantities to each other?

1. tells you the degrees of freedom of the system, 2. the constraints upon the system.
 


For number one,obviously there are three spatial quantities for describing the particle's position for the particle in three dimension and two for the particle in plane. However I am sorry that I couldn't figure out the second one.
 


Suppose the plane the particle is to move on lies in a 3-D world.

How many constraints are then put on the particle's motions?
 


I guess it is two
 


roshan2004 said:
I guess it is two
Why?

How many equations in x,y and z are needed to specify a particular plane?
 


Three
 


Do you even know how to specify a plane with the help of equation(s)??
 


in the form of ax+by+cz=0
 
  • #10


roshan2004 said:
in the form of ax+by+cz=0

And how many equations is that expression??
 
  • #11


only one
 

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