The Race Rotational Kinetic Energy The Forgotten Kinetic

Rotational Kinetic Energy The Forgotten Kinetic Energy

ENERGY l What is Energy? l The l ability of an object to do

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

CONSERVATION OF ENERGY “The law of conservation of energy states that the total amount

MOMENT OF INERTIA l What is Inertia? l l An object’s tendency to remain

MOMENT OF INERTIA l Depending on the axis of rotation, different objects have different

ANGULAR VELOCITY Angular Velocity (rad/s) is a pseudo-vector which specifies the angle traveled per

ANGULAR VELOCITY Where: • 2π = one rotation in radians • v = translational

WHAT IS THE VELOCITY OF EACH OBJECT AT THE BOTTOM OF THE RAMP? KE

THE ANSWER: Conservation of Energy Remember the conservation of energy. Make sure you state

THE ANSWER: Rotational Kinetic Energy Use the Moment of Inertia from the list and

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

THEORY vs PRACTICE l Do our theoretical values match up with our measured values?

CONCEPTUAL QUESTIONS l If they were to roll up an incline right after, what

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The Race

Rotational Kinetic Energy The Forgotten Kinetic Energy

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

KINETIC ENERGY l Translational Kinetic Energy l Rotational Kinetic Energy l 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. ”

ANALYSING THE DEMO…

EQUATION REPRESENTATION

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

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

Tangential Velocity B 1 > A 1 B 2 > A 2

EQUATION REPRESENTATION

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 • v = translational velocity • t = time for one rotation • r = radius of tire

WHAT IS THE VELOCITY OF EACH OBJECT AT THE BOTTOM OF THE RAMP? KE Rotational h =. 0806 m r = r 1 =. 025 m = R r 2 =. 02 m <- ignore for Solid Cylinder g = 9. 81 m/s 2

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. Velocity of Solid Cylinder: 1. 03 m/s Velocity of Hollow Cylinder: 0. 932 m/s Velocy of Hoop: 0. 889 m/s

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

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

QUESTIONS?