# LEMMA Rotational Dynamics

At the start of the physics tutorial, the navigation bar will hold a couple of icons, which lead to topics that the students should be already familiar with (e.g. "Crossproduct"). The student can always go back to those topics review the particular subtutorial again.

The first scheduled subtutorial to come up covers the topic

**"Angular momentum"** which is the analog of linear momentum in rotational motion. The system visualizes a particle (part of a bigger rigid body) with an axis of rotation. The student can then draw a coordinate system. At first the student will setup the coordinate system following the systems instructions. Later the system will encourage to choose another coordinate system for showing that the transfered knowledge is applicable for any setup (This action might in some setups be restricted though, if it would make the issue too complicated if it could be drawn anywhere). Coworking with the student, the particle is being spun round the axis as the student creates a force on it (pulls out a vector). Introducing more particles that make in the end a rigid body, we show that the total angular momentum of the body can be obtained by summing up all the single momenta. Moving the coordinate system will show the student that individual angular momenta depend on the location of the origin while the overall angular mometum of a axis symetrical rigid body always stays the same.

The second subtutorial coming up is about

**"Torque"**: Torque is the change of Angular momentum over time. Applying a force F at a spinning rigid body at Point P with at position r creates a torque t that can be calculated as t = r x F. We visualize a non-spinning body and let the student apply a force at a designated point of the body. This force will create a torque which can be visualized as vectors and in formula / numbers. Then the simulation starts and the body begins to spin, showing the change of angular momentum (and velocity). If the body is axis symetrical, every particle on the oposite side experiences the same force in oposite direction, resulting in a "counter torque". Adding these torques results in a overall torque that is parallel to the axis of rotation. Thats why in that case the torque changes the magnitude of angular momentum. The next visualization shows a body, that is already in motion and the student can again apply a force, seeing that when she applies it tangential to the circle that P rotates through, the angular momentum will just increase/decrease in magnitude -> the body spins faster/slower. The same experiment is done once more with the coordinate system in another place to show that the calculation does not depend on its position/orientation. That is because torque and angular momentum are related in the same way to the coordinate system. So when you change it, this does change the representation of torque but in the same step the representation of linear momentum is changed accordingly. The system can show that on the fly, what makes it easier for the student to understand. The concept of Torque changing angular momentum is shown using a visualization of a pendulum. The Torque points in a different direction as the pendulum is moving past its lowest point and therefore starts to change angular momentum in the other direction.

A third subtutorial is about

**"Precession"**. It combines the two others and shows that torque changes angular momentum not only in magnitude, but also in direction if the torque has a component that is not parallel to the angular momentum. A spinning top is visualized that rotates around an axis that is not perpendicular to the surface. So gravity is applying a torque to the body, that makes its angular momentum change direction. As a spinning top is sysmetrical about its axis of rotation, this axis "follows" angular mometum to keep it balanced. The spinning top therefore rotates around a second axis that is perpendicular to the surface.