Modeling rotational motion with differential equations

[idrivehiscar]

Hi all,

I'm new to the forums, so forgive me if I'm posting in the wrong place.

Strictly speaking, this isn't a "homework" question in that I'm not presenting a specific problem to be solved...But I have been assigned a project (due in a week...damn you, procrastination!) that involves some creativity. The professor asked us to present the material covered in the course in a new format, relating it to a personal interest. I've chosen to relate differential equations to ballet- specifically to modeling the way a dancer turns. Problem is, I have no idea where to start.

So, I implore you:

How could one model, using information such as the weight of the dancer, her center of mass, and the force she pushes off the ground with, how many pirouettes she could execute before coming to a stop? I assume the problem would work similarly to the mass-spring problem, although rather than oscillations there are turns, and factors like air resistance and friction would replace damping.

So...any ideas where to start? Any web references that could help me out? Or should I scrap the project and pick something different?

Please please please help :)

 

[AiRAVATA]

Why don't you read about the spinning top?

 

[tacman]

Hi there! Modeling rotational motion with differential equations is a fascinating topic, and I think it's great that you've chosen to relate it to ballet. To start, you could think about the forces acting on the dancer as she turns. As you mentioned, the force she pushes off the ground with is one of the main factors, but there are also other forces at play such as air resistance and friction. You can use Newton's laws of motion to set up the differential equations for this system.

Next, you can consider the rotational dynamics of the dancer. This involves thinking about the moment of inertia, which is a measure of how difficult it is to rotate an object. In this case, the dancer's body would have a certain moment of inertia that would affect how quickly she can turn. You can also consider the angular velocity, which is the rate at which the dancer is rotating.

Once you have all these factors in place, you can set up the differential equations and solve them to determine the number of turns the dancer can execute before coming to a stop. You can also consider different scenarios, such as varying the force she pushes off with or changing her weight, to see how these factors affect her ability to turn.

As for resources, there are many online tutorials and videos that can help you understand the concepts of rotational motion and differential equations. I would also recommend consulting with your professor or a TA for guidance and advice. With some effort and creativity, I'm sure you can come up with a great project that combines your interest in ballet with the material covered in your course. Good luck!