Mary and Claire find the distance traveled by the tips of the blades of two wind turbines. They relate those arc lengths to the angles of rotation made by the blades.
Episode Supports
Students’ Conceptual Challenges
While Claire and Mary seemed ready to complete this task, some students might struggle to come to the same conclusions as the students in the video. The relationship between angle of rotation and arc length cannot be easily determined without knowing the radius of the circle. Put differently, as Mary and Claire said, a larger turbine blade will carve out a longer arc length given some set angle of rotation compared to a smaller turbine blade. Use this task and the prompts below to help your students reach a similar conclusion.
Focus Questions
For use in a classroom, pause the video and ask these questions:
[Pause the video at 0:40] Before watching Mary and Claire tackle this task, try it for yourself. Consider two wind turbines, one with blades that measure 350 ft and another with blades that measure 125 ft. If it takes each turbine 5 seconds to make one full rotation, find how far each blade has traveled after 3 seconds. After exploring this task, compare your work to Mary and Claire’s.
After watching the video, consider the angles of rotation made by one blade on each of the turbines. How do the two angles of rotation compare?
Supporting Dialogue
[Pause the video at 2:57] With a partner, summarize the plan for completing the task that Mary and Claire have developed. How does it compare to your method for finding how far each blade has traveled?
[Pause the video at 8:59] What did Claire and Mary say about why the larger blade travels farther in the same amount of time? Do you agree with them? What other ideas do you have that might explain why the larger blade travels farther in the same amount of time as the smaller blade?
