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## The Race

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**Rotational Kinetic Energy**The Forgotten Kinetic Energy**ENERGY**• What is Energy? • The ability of an object to do work. • What are the two Forms of Energy? • Potential Energy • Kinetic Energy**KINETIC ENERGY**• Translational Kinetic Energy • Rotational Kinetic Energy • Vibrational Kinetic Energy**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.”**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.**MOMENT OF INERTIA**• Depending on the axis of rotation, different objects have different moments of inertia.**Tangential Velocity**B1 > A1 B2 > A2**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.**ANGULAR VELOCITY**• Where: • 2π = one rotation in radians • t = time for one rotation • Where: • v = translational velocity • r = radius of tire**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**THE ANSWER: Conservation of Energy**Remember the conservation of energy. Make sure you state it and then Setup the rest of your equations accordingly.**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.**THE ANSWER: Velocity!**The masses cancel and you can easily solve for velocity.**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**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?