Sometimes we get so used to things that we fail to appreciate just how intricately they’re designed. Take cars, for instance: when a car turns, the outer wheel has to move farther than the inner wheel. But how is that possible if the wheels are connected by an axle?

In this lesson, students use the geometry of circles to understand how we get from point A to point B when the path isn’t a straight one.

Students will

  • Sketch arcs and apply the circumference formula to calculate their lengths
  • Given the size of a tire and the turning radius of a vehicle, determine how many revolutions it makes while performing a U-turn
  • Compare the rotational speeds for wheels on different sides of a car as it turns
  • Discuss the differential, a gear mechanism that allows car wheels to rotate at different speeds
  • Compare the mechanics of how a car turns to the mechanics of how a train turns

Before you begin

Students should know the formula for the circumference of a circle (C = 2πr), and should have some experience drawing circles (using whatever level of precision you deem appropriate).

Common Core Standards

Content Standards
Mathematical Practices