• C9 – Rotational Energy General Physics 1

Two Minute Problems – C9T.2

• • • • • • • A merry-go-round makes a complete revolution once every 6.28 s. What is the speed (in meters per second) of a horse 5 m from the merry-go-round’s center?

A. 0.80 m/s B. 1.0 m/s C. 1.26 m/s D. 5.0 m/s E. 31.4 m/s F. Other General Physics 2

Two Minute Problems – C9T.4

• • • • • • • A bicyclist passes in front of you, moving perpendicular to your line of sight from your left to your right. The angular velocity of its wheels points roughly A. To your right B. To your left C. Toward you D. Away from you E. To your right at the top, to your left on the bottom F. Other General Physics 3

Two Minute Problems – C9T.7

• • • • Two wheels have the same total mass M and radius R. One wheel is a unform disk. The other is like a bicycle wheel, with lightweight spokes connecting the rim to the hub (the mass of the hub is much smaller than the mass of the rim). Which has the larger moment of intertia?

A. The solid disk B. The wheel with spokes C. There is insufficient information for a meaningful answer General Physics 4

Rotational Energy • • Which object will be moving faster at the bottom?

The potential energy must convert the same amount of potential energy to kinetic energy in each case.

General Physics 5

Angles  

r s

 General Physics 6

  Angular velocity • A particle’s rotational speed

v



ds dt v

 

ds r dt d



dt v



r

 

r

 General Physics  7

Angular velocity • The direction of angular velocity is defined by convention to be the direction along the axis indicated by your right thumb if you wrap your right fingers around the axis in the direction that the object’s particles move as the object rotates.

General Physics 8

 Moment of Inertia • Moment of Intertia •

I



m

1

r

1 2 

m

2

r

2 2  ...



m N r N

2 

N



i

 1

m i r i

2 Object’s Rotational Kinetic Energy •

K rot

 1 2

I

 2 Review exercises  • C9.1, 2, 3 General Physics 9

Translation and Rotation • An object’s total kinetic energy is the sum of it’s translational and rotational kinetic energies

K



K cm



K rot

 1 2 2

Mv CM

 1 2

I

 2  General Physics 10

Rolling without slipping • When an object is rolling without slipping, the center of mass speed equals it’s rotational speed.

v CM



R

 General Physics  11

Conservation of Energy - Ex. C9.4

• A cylindrical hoop with a mass of 2.5 kg and a radius of 0.50 m rolls from rest down a hill 25 m tall. How fast is the hoop rotating (in revolutions per second when it reaches the bottom? How fast is the hoop’s center of mass moving at this point?

General Physics 12

General Physics 13

Group Activity - Race the shapes • • A hoop, a disk, and a ball of equal radius are having a race down an incline. Who will win? Justify your answer using conservation of energy. Show all your work!!

Race the shapes down the incline and compare your results to your calculations.

General Physics 14

Group Problems • C9R.1

General Physics 15