1. Bicycles 1 Bicycles

2. Bicycles 2 Introductory Question How would raising the height of a sport utility vehicle affect its turning stability? How would raising the height of a sport utility vehicle affect its turning stability? A. Make it less likely to tip over B. Make it more likely to tip over C. Have no overall effect on its stability

3. Bicycles 3 Observations about Bicycles They are hard to keep upright while stationary They are hard to keep upright while stationary They stay upright easily while moving forward They stay upright easily while moving forward They require leaning during turns They require leaning during turns They can be ridden without hands They can be ridden without hands

4. Bicycles 4 5 Questions about Bicycles Why is a stationary tricycle so stable? Why is a stationary tricycle so stable? Why is stationary bicycle so unstable? Why is stationary bicycle so unstable? Why does a moving tricycle flip during turns? Why does a moving tricycle flip during turns? Why must you lean a bicycle during turns? Why must you lean a bicycle during turns? Why can you ride a bicycle without hands? Why can you ride a bicycle without hands?

5. Bicycles 5 Question 1 Why is a stationary tricycle so stable? Why is a stationary tricycle so stable?

6. Bicycles 6 Tricycles: Static Stability (Part 1) An upright tricycle has a base of support: An upright tricycle has a base of support: the polygon formed by its ground contact points the polygon formed by its ground contact points A tricycle has a center of gravity: A tricycle has a center of gravity: the effective point at which its weight is located the effective point at which its weight is located When center of gravity is above base of support, When center of gravity is above base of support, the tricycle is in a stable equilibrium, the tricycle is in a stable equilibrium, its gravitational potential rises whenever it’s tipped, its gravitational potential rises whenever it’s tipped, it accelerates in the direction opposite the tip, it accelerates in the direction opposite the tip, and it returns to equilibrium and it returns to equilibrium

7. Bicycles 7 Tricycles: Static Stability (Part 2) When its center of gravity isn’t above the base, When its center of gravity isn’t above the base, the tricycle is not in equilibrium, the tricycle is not in equilibrium, its gravitational potential energy drops when it tips, its gravitational potential energy drops when it tips, it accelerates in the direction of the tip, it accelerates in the direction of the tip, and it falls over and it falls over When its center of gravity is above edge of base, When its center of gravity is above edge of base, the tricycle is in an unstable equilibrium, the tricycle is in an unstable equilibrium, to which it never returns after being tipped to which it never returns after being tipped

8. Bicycles 8 Question 2 Why is stationary bicycle so unstable? Why is stationary bicycle so unstable?

9. Bicycles 9 Bicycles: Static Instability A base of support requires ≥3 contact points A base of support requires ≥3 contact points An upright bicycle has only 2 contact points An upright bicycle has only 2 contact points An upright bicycle is in an unstable equilibrium An upright bicycle is in an unstable equilibrium A stationary bicycle tips over easily A stationary bicycle tips over easily

10. Bicycles 10 Question 3 Why does a moving tricycle flip during turns? Why does a moving tricycle flip during turns?

11. Bicycles 11 Tricycles: Dynamic Instability When a tricycle is moving, When a tricycle is moving, its velocity can point opposite its acceleration, its velocity can point opposite its acceleration, so a stable equilibrium doesn’t ensure stability so a stable equilibrium doesn’t ensure stability During a high speed turn, During a high speed turn, the rider travels straight ahead, the rider travels straight ahead, the tricycle starts to tip, the tricycle starts to tip, the acceleration opposite the tip is too slow, the acceleration opposite the tip is too slow, and the tricycle tips over anyway and the tricycle tips over anyway

12. Bicycles 12 Introductory Question How would raising the height of a sport utility vehicle affect its turning stability? How would raising the height of a sport utility vehicle affect its turning stability? A. Make it less likely to tip over B. Make it more likely to tip over C. Have no overall effect on its stability

13. Bicycles 13 Question 4 Why must you lean a bicycle during turns? Why must you lean a bicycle during turns?

14. Bicycles 14 Bicycles: Dynamic Stability When a bicycle makes a high speed turn, When a bicycle makes a high speed turn, the rider’s initial velocity is straight ahead, the rider’s initial velocity is straight ahead, leaning inward makes the rider accelerate inward, leaning inward makes the rider accelerate inward, and the rider and bicycle turn together safely and the rider and bicycle turn together safely The bicycle drives under the overall center of gravity to return to the unstable equilibrium The bicycle drives under the overall center of gravity to return to the unstable equilibrium Motion can make a bicycle stable! Motion can make a bicycle stable!

15. Bicycles 15 Question 5 Why can you ride a bicycle without hands? Why can you ride a bicycle without hands?

16. Bicycles 16 A Bicycle’s Automatic Steering It naturally steers under its center of gravity It naturally steers under its center of gravity due to gyroscopic precession of the front wheel (the ground’s torque on spinning wheel steers it) due to gyroscopic precession of the front wheel (the ground’s torque on spinning wheel steers it) due to the design of its rotating front fork (the fork steers to reduce total potential energy) due to the design of its rotating front fork (the fork steers to reduce total potential energy) A forward-moving bicycle that begins to tip A forward-moving bicycle that begins to tip automatically returns to its unstable equilibrium, automatically returns to its unstable equilibrium, and thus exhibits wonderful dynamic stability and thus exhibits wonderful dynamic stability

17. Bicycles 17 Summary about Bicycles Tricycles Tricycles have static stability have static stability can flip during turns can flip during turns Bicycles Bicycles are statically unstable are statically unstable can lean during turns to avoid flipping can lean during turns to avoid flipping automatically steer back to unstable equilibrium automatically steer back to unstable equilibrium have remarkable dynamic stability have remarkable dynamic stability