Angular Motion Chapter 10. Figure 10-1 Angular Position.
-
Upload
daniela-tucker -
Category
Documents
-
view
224 -
download
0
Transcript of Angular Motion Chapter 10. Figure 10-1 Angular Position.
![Page 1: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/1.jpg)
Angular Motion
Chapter 10
![Page 2: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/2.jpg)
Figure 10-1Angular Position
![Page 3: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/3.jpg)
Figure 10-2Arc Length
![Page 4: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/4.jpg)
Figure 10-3Angular Displacement
![Page 5: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/5.jpg)
Figure 10-4Angular Speed and Velocity
![Page 6: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/6.jpg)
Angular Speed is a Vector!
We use a “right hand rule” to determine the vector direction of a rotation. Using your right hand, curl your fingers in the direction of the rotation. Your thumb points in the direction of the rotation.
Works for angular acceleration as well.
![Page 7: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/7.jpg)
Figure 10-5Angular Acceleration
![Page 8: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/8.jpg)
Summary of angular motions.
t
t
Angular position, radians, measure counter-clockwise.
Angular velocity, radians per second.
Angular acceleration, radians per second squared.
Note that radians are a dimensionless quantity.
Radians = Degrees * /180
Example: 180 degrees = 3.14 radians
![Page 9: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/9.jpg)
Linear and Rotational Motion Compared
2
2
1mvK
amF
vmP
t
va
t
xv
x
2
2
1
IK
IT
IL
t
t
Position
Velocity
Acceleration
Momentum
Force/Torque
Kinetic Energy
![Page 10: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/10.jpg)
Figure 10-7Angular and Linear Speed
![Page 11: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/11.jpg)
Conceptual Checkpoint 10-1How do the angular speeds compare?
V=r
How do the linear speeds compare?
![Page 12: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/12.jpg)
Figure 10-8Centripetal and Tangential Acceleration
IMPORTANT:For uniform circular motion, The centripetal acceleration is:
r
vac
2
For constant angular speed, at = 0. Then, the acceleration is RADIAL, inwards.
![Page 13: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/13.jpg)
Figure 10-9Rolling Without Slipping
![Page 14: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/14.jpg)
Figure 10-11Velocities in Rolling Motion
![Page 15: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/15.jpg)
Figure 10-10Rotational and Translational Motions of a Wheel
![Page 16: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/16.jpg)
Figure 10-12Kinetic Energy of a Rotating Object
2
2
1mvK
But… rv
So…
22
2
2
2
12
12
1
mr
rm
mvK
Define the moment of inertia, I…
2mrI
(it’s different for different shapes!)
2
2
1 IKROT
![Page 17: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/17.jpg)
Moment of Inertia
i
iirmI 2
Vi
Mi
Ri
I
RM
RM
VM
KK
ii
i
iiii
iii
ii
2
22
22
2
2
1
2
1
2
1
2
1
Rigid body. Break up into small pieces Mi. What is the angular speed of each piece?
![Page 18: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/18.jpg)
Rotational force: Torque
Torque is the “twisting force” that causes rotational motion. It is equal to the magnitude of the component of an applied force perpendicular to the arm transmitting the force.
F
RA
The torque around point A is T = R x F
![Page 19: Angular Motion Chapter 10. Figure 10-1 Angular Position.](https://reader036.fdocuments.in/reader036/viewer/2022062322/5697c0071a28abf838cc5f86/html5/thumbnails/19.jpg)
Example: torque’s in balance
2r 4f
2mm