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Chapter 10:  Dynamics of Rotational Chapter 10:  Dynamics of Rotational

Chapter 10: Dynamics of Rotational - PowerPoint Presentation

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Chapter 10: Dynamics of Rotational - PPT Presentation

Motion 2016 Pearson Education Inc Dynamics of Rotational Motion Conservation of angular momentum Goals for Chapter 10 Torque angular force To see how torques cause rotational dynamics just as linear forces cause linear accelerations ID: 640792

pearson angular education 2016 angular pearson 2016 education figure momentum torque rotational moment dynamics mass point force energy velocity

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Slide1

Chapter 10: Dynamics of Rotational Motion

© 2016 Pearson Education, Inc.Slide2

Dynamics of Rotational Motion

(Conservation of angular momentum)Slide3

Goals for Chapter 10

Torque: “angular force”

To see how torques cause rotational dynamics (just as linear forces cause linear accelerations)

To examine the

combination of translation and rotationTo calculate the work done by a torqueTo study angular momentum and its conservationTo relate rotational dynamics and angular momentum To study how torques add a new variable to equilibriumTo see the vector nature of angular quantities.Slide4

Rotational Dynamics: I

m

1

m

2

m

3Slide5

The figure shows two equal-mass blocks suspended by a cord of negligible mass that runs over a pulley with half the mass of a block. The blocks are moving with constant velocity. How do the magnitudes of the forces and exerted by the cord on the two sides of the pulley compare?

a) They are equal.

b)

F

A > FBc) FA < FB© 2016 Pearson Education, Inc.

Clicker questionSlide6

Definition of Torque – Figure 10.1Torque (

) is defined as the force applied multiplied by the moment arm.

The moment arm is the perpendicular distance from the point of force application to the pivot point.

© 2016 Pearson Education, Inc.Slide7

A Plumbing Problem to Solve – Example 10.1

 

© 2016 Pearson Education, Inc.Slide8

Torque

Note: F(rad)has no torque with respect to OSlide9

There Is a Sign Convention – Figure 10.3A counterclockwise force is designated as positive (+).

A clockwise force is designated as negative (−).

© 2016 Pearson Education, Inc.Slide10
Slide11
Slide12

Note: t

= F R sinqSlide13

Note: sign of tSlide14

 Slide15

 Slide16

 Slide17

Why Do Acrobats Carry Long Bars? Refer to the photo caption on the bottom of page 287.

© 2016 Pearson Education, Inc.Slide18

Rotating Cylinders Clicker Question

Relationship of torque and angular acceleration

rotational analog of Newton’s law

Which choice correctly ranks the magnitudes of the angular accelerations of the three cylinders?A.

B.

C.

D.

 

© 2016 Pearson Education, Inc.Slide19

Unwinding a Winch (Again) – Example 10.2

 

© 2016 Pearson Education, Inc.Slide20

 

A Bowling Ball Rotates on a Moving Axis – Example 10.5

© 2016 Pearson Education, Inc.Slide21

Work and power in rotational motionSlide22

The block in the figure slides in a circle on a nearly frictionless table with a speed v. You hold it by means of a string passing through a hold in the table. If you raise your hand so that the radius of the block

's circle doubles, the block

'

s final speed will be

2v.1/2v.1/4v.d) v.© 2016 Pearson Education, Inc.

Clicker questionSlide23

Angular momentumSlide24

Angular Momentum Is Conserved –Figure 10.19

The first figure shows the figure skater with a large moment of inertia.

In the second figure, she has made the moment much smaller by bringing her arms in.

Since

L is constant, must increase.© 2016 Pearson Education, Inc.Slide25

Conservation of angular momentum

5 kg

L=r

x

p

|L|=(rp)sin90=(r)(mv)

 

v=r

 

 

Conservation of LSlide26

Angular Momentum – Figure 10.15The diver changes rotational velocities by changing body shape.

The total angular momentum is the moment of inertia multiplied by the angular velocity.

© 2016 Pearson Education, Inc.Slide27

Equilibrium

condition for equilibrium

Center of gravity is the turning point Slide28

A New Equilibrium Condition – Figure 10.24Now, in addition to , we also must add

© 2016 Pearson Education, Inc.Slide29

Balancing on a Teeter-Totter – Figure 10.26

The heavier child must sit closer to balance the torque from the smaller child.

Your torque is

Your friend is

from the pivot, and her torque is:

For equilibrium,

.

 

© 2016 Pearson Education, Inc.Slide30

Walking the plank

 Slide31
Slide32

A fishy wind chime

 Slide33

Hanging a farm gate

 Slide34

Carrying a box up the stairs

 

FSlide35

How a car’s clutch work

The clutch disk and the gear disk is pushed into each other by two forces that do not impart any torque, what is the final angular velocity when they come together?Slide36
Slide37

Problem 10.74

What is the original kinetic energy

K

i

of disk

A?

Initially

;

and

Final;

(after coupling together)

Conservation of angular momentum;

Final Kinetic energy;

(thermal energy developed during coupling)

So, original energy;

 Slide38

Honda 600RR

Who races this bike?

Why can anybody race it, if he just

dares to go fast?

The oval track of the Texas

World Speedway allows speeds

of 250 mph. Slide39

Angular Quantities Are Vectors –Figure 10.29

The "right-hand rule

"

gives us a vector

's direction.© 2016 Pearson Education, Inc.Slide40

Vector nature of angular quantitiesSlide41

A non rotating and rotating gyroscopeSlide42

 

Analogous to

 

 

 

rad/s

 

is the weight of the flywheel, and

is the distance from the pivot point of the center of mass of the flywheel.

 

Precesion Angular Velocity

 Slide43