Angular momentum

1
Angular momentum

• Relationship between angular momentum and linear
  momentum is the same as between torque and force.

2
Units

• The units for angular momentum are
  kg-m2/s

3
Angular momentum of rigid objects

• Look at L for one particle of the object

• Sum over all particles for total angular momentum

4
Example

• A woman with mass 50 kg is standing on the rim of
  a large disk that is rotating at 0.50 rev/s about
  an axis through its center. The disk has mass
  110 kg and a radius of 4.0 m. Calculate the
  magnitude of the total angular momentum of the
  woman-plus-disk system. You can treat the woman
  as a point.
• 5275 kg-m2/s

5
On your own

• Find the magnitude of the angular momentum of the
  sweeping second hand on a clock about an axis
  through the center of the clock face. The clock
  hand has a length of 15.0 cm and a mass of 6.00
  g. Take the second hand to be a slender rod
  rotating with constant angular velocity about one
  end.
• 4.71 x 10-6 kg-m2/s

6
Conservation of angular momentum

• If there is no net external torque acting on a
  system, then the total angular momentum of the
  system is conserved.

7
Example

• A uniform circular disk is rotating with an
  initial angular speed w1 around a frictionless
  shaft through its center. Its moment of inertia
  is I1. It drops onto another disk of moment of
  inertia I2 that is initially at rest on the same
  shaft. Because of surface friction between the
  disks, they eventually attain a common angular
  speed wf. Find wf.