# What are kinetic and geometric constraints?

• freutel
In summary, the question is asking for all forces and constraints in a two-seat merry go round model, using generalised coordinates (θ, φ, and x). The forces include the gravitational force (mg) and the centripetal force (m(L+x)(dθ/dt)^2), while the constraints may include the fact that the pendulum sticks can rotate horizontally around the central vertical axis (described by φ) and can also move relative to the central vertical pole (described by θ). It may be helpful to use Lagrangian mechanics to solve this problem.
freutel

## Homework Statement

The question is to specify all forces and constraints that are applied in a system of a two-seat merry go round model in terms of the generalised coordinates - and their type (e.g. geometric, kinetic).

http://i.imgur.com/FQ7PJyg.png

The system is modeled as central vertical rotation axis, with two identical pendulum-sticks attached to its top. Each pendulum is a (weightless) elastic stick of length L with a point-mass mattached to its end. The elastic sticks have a spring constant K [N/m]. The sticks are free to rotate horizontally around the central vertical axis (described by an angle φ), and can also move relative to the central vertical pole (indicated by angle θ in below Figure). The generalised coordinates are the two angles θ and φ [in radians] and extension x [in meters] of both sticks.

## Homework Equations

I have no idea what the relevant equations for this problem are. I think these equations may be relevant:
• F=ma
• Fcentripetal=mv2/r
• v=rω

## The Attempt at a Solution

So first to specify all the forces there is the gravitational force of the point masses which is always mg. I guess this is geometric. Than you have the centripetal force. The angular velocity is de time derivative of angle θ and the radius is length L + extension x. So centripetal force can be written as Fcentripetal=mrω2 --> m(L+x)(dθ/dt)2. And I guess this is kinetic.
This is about everything I can come up with for this question but there are still some unanswered things. What is a constraint (both geometric and kinetic) and what does angle φ stand for? The reason I ask what angle φ stands for is because I don't get the description "The sticks are free to rotate horizontally around the central vertical axis (described by an angle φ)". The picture doesn't show an angle φ so that's why I am confused. A little help would be appreciated.

freutel said:
The question is to specify all forces and constraints that are applied in a system of a two-seat merry go round model in terms of the generalised coordinates - and their type (e.g. geometric, kinetic).

I think you are working on Lagrangian mechanics so think about Lagrangian function of action.

freutel said:
the gravitational force of the point masses which is always mg. I guess this is geometric.
I believe the "type (e.g. geometric, kinetic)" refers to constraints, not to forces. Certainly I would not describe mg as 'geometric'.
freutel said:
Than you have the centripetal force.
It asks for "all forces and constraints that are applied". Centripetal force is not an applied force. I guess you could characterise it as a constraint.
freutel said:
what does angle φ stand for?
To see angle φ you need to look at the plan view, i.e. what does it look like from above? ##\dot\phi## would be the angular velocity about the vertical axis.
freutel said:
The angular velocity is de time derivative of angle θ
That's the angular velocity about a horizontal axis perpendicular to the plane containing the pendulum 'sticks'.
At any instant, both φ and θ may be changing, so the overall angular velocity is the vector sum of the two.

## 1. What is the difference between kinetic and geometric constraints?

Kinetic constraints refer to restrictions on the movement or motion of particles, molecules, or objects. These can include limitations on speed, direction, or range of motion. Geometric constraints, on the other hand, refer to restrictions on the shape, size, or position of objects. These can include fixed angles, specific dimensions, or fixed positions.

## 2. How do kinetic and geometric constraints impact physical systems?

Kinetic and geometric constraints play a crucial role in determining the behavior and properties of physical systems. They can affect the stability, flexibility, and overall function of these systems. For example, in a chemical reaction, kinetic constraints can determine the rate at which reactants turn into products, while geometric constraints can determine the shape and stability of the resulting molecules.

## 3. Can kinetic and geometric constraints be manipulated or controlled?

Yes, kinetic and geometric constraints can be manipulated or controlled in various ways. In science and engineering, researchers often use different techniques and methods to alter these constraints in order to achieve specific outcomes or optimize the performance of a system. For example, changing the temperature or pressure in a reaction can alter the kinetic constraints and affect the rate of the reaction.

## 4. Are there any real-life examples of kinetic and geometric constraints?

Yes, there are many real-life examples of kinetic and geometric constraints. In sports, for instance, the rules and regulations of a game act as geometric constraints that determine the size and shape of the playing field, while the physical abilities and limitations of players act as kinetic constraints on their movements and actions. Another example is in construction, where specific geometric constraints must be followed to ensure the stability and safety of a building.

## 5. How are kinetic and geometric constraints related to the laws of physics?

Kinetic and geometric constraints are closely related to the laws of physics, specifically the laws of motion and thermodynamics. These constraints are based on fundamental principles of physics, such as conservation of energy and momentum, and dictate how particles and objects behave in a physical system. Understanding and manipulating these constraints is essential in advancing our understanding of the physical world and developing new technologies.

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