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# The Race

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1. The Race

2. Rotational Kinetic Energy The Forgotten Kinetic Energy

3. ENERGY • What is Energy? • The ability of an object to do work. • What are the two Forms of Energy? • Potential Energy • Kinetic Energy

4. KINETIC ENERGY • Translational Kinetic Energy • Rotational Kinetic Energy • Vibrational Kinetic Energy

5. CONSERVATION OF ENERGY “The law of conservation of energy states that the total amount of energy in an isolated system remains constant. A consequence of this law is that energy cannot be created or destroyed.”

6. ANALYSING THE DEMO…

7. ANALYSING THE DEMO…

8. ANALYSING THE DEMO…

9. ANALYSING THE DEMO…

10. EQUATION REPRESENTATION

11. MOMENT OF INERTIA • What is Inertia? • An object’s tendency to remain in whatever state it is in. • Moment of Inertia • A measure of an object’s resistance to rotational motion. • Analogous to Mass • Mass dictates the degree of Translational Inertia; Moment of Inertia dictates the degree of Rotational Inertia.

12. MOMENT OF INERTIA • Depending on the axis of rotation, different objects have different moments of inertia.

13. Tangential Velocity B1 > A1 B2 > A2

14. EQUATION REPRESENTATION

15. ANGULAR VELOCITY Angular Velocity (rad/s) is a pseudo-vector which specifies the angle traveled per unit time (s). Where: t = the time for one rotation. r = radius of the tire.

16. ANGULAR VELOCITY • Where: • 2π = one rotation in radians • t = time for one rotation • Where: • v = translational velocity • r = radius of tire

17. WHAT IS THE VELOCITY OF EACH OBJECT AT THE BOTTOM OF THE RAMP? h = .0806 m r = r1 = .025 m = R r2 = .02 m <- ignore for Solid Cylinder g = 9.81 m/s2 KE Rotational

18. THE ANSWER: Conservation of Energy Remember the conservation of energy. Make sure you state it and then Setup the rest of your equations accordingly.

19. THE ANSWER: Rotational Kinetic Energy Use the Moment of Inertia from the list and the Angular Velocity in terms of Translational Velocity to find the Rotational Kinetic Energy.

20. THE ANSWER: Velocity! The masses cancel and you can easily solve for velocity.

21. THEORY vs PRACTICE • Do our theoretical values match up with our measured values? • If not, are they within reason? • What are some reasons they are different? • Friction • A digital Camera is not very accurate. • Location might not be exactly 8cm off the table

22. CONCEPTUAL QUESTIONS • If they were to roll up an incline right after, what height would they stop at? • What would the velocity of the objects be if the ramp were frictionless?

23. QUESTIONS?