Class 29 Rolling, Torque and Angular Momentum

1
Class 29 - Rolling, Torque and Angular
Momentum Chapter 11 - Monday November 1st

• Review of Newton's second law in angular form
• Conservation of angular momentum
• Demos and sample problems

Reading pages 275 thru end of Part I of HRW Read
and understand the sample problems Assigned
problems from chapter 11 (due at 11pm on Sunday
November 7th) 2, 6, 8, 12, 22, 24, 32, 38, 40,
50, 54, 64
2
Torque and angular momentum

• Torque was discussed in the previous chapter
  cross products are discussed in chapter 3
  (section 3-7) and at the end of this
  presentation torque also discussed in this
  chapter (section 7).

• Here, p is the linear momentum mv of the object.

3
Newton's second law in angular form
The vector sum of all the torques acting on a
particle is equal to the time rate of change of
the angular momentum.
For a system of particles
4
The Gyroscope
Used in navigational devices - even modern ones.
5
The Gyroscope
Used in navigational devices - even modern ones.
6
Conservation of angular momentum
It follows from Newton's second law that
If the net external torque acting on a system is
zero, the angular momentum of the system remains
constant, no matter what changes take place
within the system.
7
Conservation of angular momentum
It follows from Newton's second law that
If the net external torque acting on a system is
zero, the angular momentum of the system remains
constant, no matter what changes take place
within the system.
What happens to kinetic energy?

• Thus, if you increase w by reducing I, you end up
  increasing K.
• Therefore, you must be doing some work.
• This is a very unusual form of work that you do
  when you move mass radially in a rotating frame.
• The frame is accelerating, so Newton's laws do
  not hold in this frame