Post on 21-Jan-2016
transcript
Angular Motion
Chapter 10
Figure 10-1Angular Position
Figure 10-2Arc Length
Figure 10-3Angular Displacement
Figure 10-4Angular Speed and Velocity
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.
Figure 10-5Angular Acceleration
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
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
Figure 10-7Angular and Linear Speed
Conceptual Checkpoint 10-1How do the angular speeds compare?
V=r
How do the linear speeds compare?
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.
Figure 10-9Rolling Without Slipping
Figure 10-11Velocities in Rolling Motion
Figure 10-10Rotational and Translational Motions of a Wheel
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
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?
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
Example: torque’s in balance
2r 4f
2mm