The physical orientation of a ski or snowboard may change dramatically during a sport. These changes may include rotation in the x, y, and z axes of a full 360 degrees or more.
What does rotation look like in a graph? Consider the graph below, excerpted from a book series by Schottenbauer Publishing.
Discussion Questions
- How many rotations are shown on the graph?
- Identify the time segments of each of the rotations.
- What is the length of the time of each rotation?
- Describe each rotation in terms of degrees or radians of rotation in the x, y, and z axes.
- [Advanced Question] Describe each rotation in terms of angular coordinates.
- What is the angular velocity of each rotation?
- What would the graph look like if the skateboard were rotated the opposite direction around the center axis? Sketch the graphs.
- What would the graph look like if the skateboard were rotated around the other two axes? Sketch the graphs.
Additional Information
Schottenbauer Publishing
Geometry is essential for snow sports. Take a moment to write down a few ways in which geometry affects the precision of the sport.
Discussion Questions
- What data is necessary to collect in order to understand the role of geometry in snow sports?
- What spatial perspectives and/or mathematical planes are important for precision?
The cover of The Geometry of Winter Olympic Sports, to the right above, features a cross-country skier in action.
Discussion Questions
- What angles can be measured on the diagram, in order to understand the accuracy of technique?
- Is any essential information missing from the picture? What is necessary in order to measure that information?
Geometry diagrams featuring snow sports are available in the following book from Schottenbauer Publishing:
Geometry Workbooks
Additional Information
Ski jumps are impressive aerial displays of the laws of physics. Studying jumps in the laboratory, without the presence of wind, presents data which is easier to analyze.
The following graph is excerpted from Volume 4 of The Science of Snow Sports from Schottenbauer Publishing.
Discussion Questions
- Using a red pen, separate the graph into the following segments: (a) At Rest on Top of Slope, (b) Trajectory on Slope, (c) Trajectory in Air, (d) Trajectory on Ground, (e) At Rest on Ground.
- Create a table with the above categories, including: (a) Initial Time, (b) Ending Time, (c) Highest x Value, (d) Lowest x Value, (e) Highest y Value, (f) Lowest y Value.
- Using the above information, calculate the average velocity during the trajectory on the slope in terms of the speed in the x direction, the y direction, and overall.
- Using the above information, calculate the average velocity in the air in terms of the speed in the x direction, the y direction, and overall.
- What occurs after the model skier hits the ground?
Additional data on snow sports can be found in the following science lab manuals from Schottenbauer Publishing:
Graphs & Data for Science Lab: Multi-Volume Series
- The Science of Snow Sports
- Volume 1: Force, Acceleration, & Video Analysis (Outdoor Snow & Lab)
- Volume 2: Force & Video Analysis (Plastic Models in Lab)
- Volume 3: Force & Acceleration (Ice-Topped Snow)
- Volume 4: Video Analysis (Models on Curved Surfaces in Lab)
Anthologies of 28 Graphs
- The Science of Winter Olympic Sports
Graphs & Data for Science Lab: Multi-Volume Series
- The Science of Athletic Training
- The Science of Exercise Equipment
- The Science of Gymnastics
- The Science of Yoga, Pilates, & Ballet
Anthologies of 28 Graphs
- The Science of Physical Fitness
- The Science of Gymnastics
- The Science of Yoga
- The Science of Dance & Ballet
Additional Information
