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?