The Race

Rotational Kinetic Energy The Forgotten Kinetic Energy

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

KINETIC ENERGY Translational Kinetic Energy Translational Kinetic Energy Rotational Kinetic Energy Rotational Kinetic Energy Vibrational Kinetic Energy Vibrational Kinetic Energy

CONSERVATION OF 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.”

ANALYSING THE DEMO…

EQUATION REPRESENTATION

MOMENT OF INERTIA What is Inertia? What is Inertia? An object’s tendency to remain in whatever state it is in. An object’s tendency to remain in whatever state it is in. Moment of Inertia Moment of Inertia A measure of an object’s resistance to rotational motion. A measure of an object’s resistance to rotational motion. Analogous to Mass Analogous to Mass Mass dictates the degree of Translational Inertia; Moment of Inertia dictates the degree of Rotational Inertia. 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. Depending on the axis of rotation, different objects have different moments of inertia.

Tangential Velocity B1 > A1 B2 > A2

EQUATION REPRESENTATION

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

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 = r 1 =.025 m = R r 2 =.02 m <- ignore for Solid Cylinder g = 9.81 m/s 2 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! Velocity of Solid Cylinder:1.03 m/s Velocity of Hollow Cylinder:0.932 m/s Velocy of Hoop:0.889 m/s The masses cancel and you can easily solve for velocity.

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

QUESTIONS?