The RaceThe Race

Rotational Kinetic EnergyRotational Kinetic Energy

The Forgotten Kinetic EnergyThe Forgotten Kinetic Energy

ENERGYENERGY

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 EnergyPotential EnergyKinetic EnergyKinetic Energy

KINETIC ENERGYKINETIC ENERGY

Translational Kinetic Translational Kinetic EnergyEnergy

Rotational Kinetic Rotational Kinetic EnergyEnergy

Vibrational Kinetic Vibrational Kinetic EnergyEnergy

CONSERVATION OF ENERGYCONSERVATION OF ENERGY

““The The law of conservation of energylaw of conservation of energy states states that the total amount of energy in an that the total amount of energy in an isolated system remains constant. A isolated system remains constant. A

consequence of this law is that energy consequence of this law is that energy cannot be created or destroyed.”cannot be created or destroyed.”

ANALYSING THE DEMO…ANALYSING THE DEMO…

ANALYSING THE DEMO…ANALYSING THE DEMO…

ANALYSING THE DEMO…ANALYSING THE DEMO…

ANALYSING THE DEMO…ANALYSING THE DEMO…

EQUATION EQUATION REPRESENTATIONREPRESENTATION

MOMENT OF INERTIA MOMENT OF INERTIA

What is Inertia?What is Inertia? An object’s tendency to remain in whatever state it is An object’s tendency to remain in whatever state it is

in.in.

Moment of InertiaMoment of Inertia A measure of an object’s resistance to rotational A measure of an object’s resistance to rotational

motion.motion. Analogous to MassAnalogous to Mass

Mass dictates the degree of Translational Inertia; Moment of Mass dictates the degree of Translational Inertia; Moment of Inertia dictates the degree of Rotational Inertia.Inertia dictates the degree of Rotational Inertia.

MOMENT OF INERTIAMOMENT OF INERTIA

Depending on the axis of rotation, different Depending on the axis of rotation, different objects have different moments of inertia.objects have different moments of inertia.

Tangential VelocityTangential Velocity

B1 > A1B2 > A2

EQUATION EQUATION REPRESENTATIONREPRESENTATION

ANGULAR VELOCITYANGULAR 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 VELOCITYANGULAR 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 WHAT IS THE VELOCITY OF EACH OBJECT AT THE BOTTOM OF THE OBJECT AT THE BOTTOM OF THE

RAMP?RAMP?

h = .0806 mh = .0806 m

r = rr = r11 = .025 m = R = .025 m = R

rr22 = .02 m <- ignore = .02 m <- ignore for Solid Cylinderfor Solid Cylinder

g = 9.81 m/sg = 9.81 m/s22

KE Rotational

THE ANSWER: Conservation of EnergyTHE ANSWER: Conservation of Energy

Remember the conservation of energy. Make sure you state it and thenSetup the rest of your equations accordingly.

THE ANSWER: Rotational Kinetic THE ANSWER: Rotational Kinetic EnergyEnergy

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 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 PRACTICETHEORY vs PRACTICE

Do our theoretical values match up with our Do our theoretical values match up with our measured values?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? FrictionFriction A digital Camera is not very accurate.A digital Camera is not very accurate. Location might not be exactly 8cm off the tableLocation might not be exactly 8cm off the table

CONCEPTUAL QUESTIONSCONCEPTUAL QUESTIONS

If they were to roll up an incline right after, If they were to roll up an incline right after, what height would they stop at?what height would they stop at?

What would the velocity of the objects be if What would the velocity of the objects be if the ramp were frictionless?the ramp were frictionless?

QUESTIONS?QUESTIONS?