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

In summary, there are different numbers of constraints and equations depending on whether the particle is moving in a plane or in three-dimensional space. For a particle in three-dimensional space, there are three spatial quantities needed to determine its position as a function of time, and therefore three degrees of freedom. For a particle in a plane, there are only two spatial quantities needed and two degrees of freedom. The number of equations also varies, with three equations needed to specify a plane in three-dimensional space and only one equation needed in the form of ax+by+cz=0.
  • #1
roshan2004
140
0
How many constraints are there when the particle is moving in a plane and on three dimensional space and what are they?
 
Physics news on Phys.org
  • #2


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.
 
  • #3


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.
 
  • #4


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?
 
  • #5


I guess it is two
 
  • #6


roshan2004 said:
I guess it is two
Why?

How many equations in x,y and z are needed to specify a particular plane?
 
  • #7


Three
 
  • #8


Do you even know how to specify a plane with the help of equation(s)??
 
  • #9


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
 

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

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

There are usually 3 constraints when a particle is moving in a plane: 2 positional constraints and 1 tangential constraint. These constraints restrict the movement of the particle in the x and y directions, as well as the direction of its velocity.

2. What is a positional constraint?

A positional constraint restricts the position of the particle in a certain direction. For example, if the particle is moving on a horizontal plane, there may be a constraint that it cannot move below a certain height.

3. What is a tangential constraint?

A tangential constraint restricts the direction of the particle's velocity. It can be thought of as a "path constraint" that the particle must follow in order to stay within a specific trajectory.

4. Can constraints limit the speed of the particle?

Yes, constraints can also limit the speed of the particle. This can be seen in situations where a particle is moving in a circular motion and there is a constraint that restricts its speed at a certain point in the circle.

5. How do constraints affect the motion of a particle in a plane?

Constraints can greatly affect the motion of a particle in a plane, as they restrict the particle's movement and can change its velocity. Constraints can also influence the shape of the particle's trajectory, making it more complex than a simple straight line or curve.

Similar threads

Replies
11
Views
2K
Replies
1
Views
805
Replies
4
Views
1K
Replies
1
Views
1K
Replies
5
Views
1K
Replies
2
Views
861
Back
Top