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
Download Presentation The PPT/PDF document "Chapter 10: Dynamics of Rotational" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
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.Slide10Slide11Slide12
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
Slide31Slide32
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?Slide36Slide37
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