Angular Velocity

1
Angular Velocity
See Active Figure 10.4 at pse6.com
2
Tangential (Linear) Velocity
vt wr Unit m/s
3
Tangential Acceleration
at ar
4
Comparison of Angular and Linear Quantities

• Make the following replacements

5
Comparison of Linear and Angular Quantities (2)
6
Equations of Constant Angular Acceleration

• Solve below problems similar to solution of
  constant acceleration problems in Chap. 2
• w wo at
• q wot ½at2
• w2 wo2 2a q

7
Definition of Torque
t Fd t force X lever arm
t Frsinf
Units of torque N-m
8
Table of Moments of Inertia for Various
Objects(1)
9
Table of Moments of Inertia for various objects(2)
10
Newtons 2nd Law for Rotations
F ma Fr mar Fr m(ar)r t (mr2)a t Ia
11
Definition of Angular Momentum Vector Method
12
Definition of Angular Momentum use of moment of
inertia
L Iw mvrsinf
13
Conservation of Angular Momentum

• If a system does not experience any
• net external torque, the angular momentum, L, of
  the system is constant
• Iowo Ifwf
• Note when solving these conservation of angular
  momentum problems, you may use whatever units are
  given .

14
Example of Conservation of Angular Momentum (1)
See Active Figure 11.3 at pse6.com
15
Example of Conservation of Angular Momentum (2)
16
Example of Conservation of Angular Momentum (3)
17
Example of Conservation of Angular Momentum (4)
18
Precession of a top
An example of this is the precession, or wobbling
of the earths axis every 26,000 years. This
means that Polaris, the current North Star,
will not be the north star in thousands of years.
Precession occurs when a net torque acts on the
CM of the top, such as gravity does here.