Transcript Document

Angular Momentum III
•
•
General motion of a rigid body + collisions
More examples
Text Section 11.1-11.6
Physics 1D03 - Lecture 31
Example 1
Comet Halley moves about the Sun in an elliptical orbit, which it’s closest
approach to the sun being about 0.590 AU (1 AU = astronomical unit, the
Earth-Sun distance). The comet’s speed at closest approach is 54.0 m/s. At
its greatest distance the comet is 35.0 AU away from the Sun (past Neptune).
What is the comet’s speed when it is farthest from the sun?
Physics 1D03 - Lecture 31
Example 2
Physics 1D03 - Lecture 31
Example 3
A solid cube of side 2a (moment of inertia for a cube of side s is I=1/6 ms2) and
mass M is sliding on a frictionless surface with constant velocity. It hits a small
obstacle (inelastic collision) at the end of the table that causes the cube to tilt
over as shown.
Find the minimum speed that the cube needs to tip over and fall of the table.
Physics 1D03 - Lecture 31
Example 4
Physics 1D03 - Lecture 31
Recall:
Angular momentum” is the rotational analogue of linear
momentum.
 external
dL

 I
dt
Hence, we should have a similar quantity to impulse in linear
momentum (I = FΔt =Δp):
dt  dL
  dt   dL
t  L
This ΔL is a ‘rotational impulse’.
Physics 1D03 - Lecture 31
Example 5
Physics 1D03 - Lecture 31
Example 6
A space station in the shape of a ring of mass 5.00x104 kg and a radius of
100 m is set into rotation by firing two small rockets attached tangentially to
opposite points on the rim of the ring. The station is set rotating about its axis
so that people inside experience an effective free-fall acceleration equal to g.
a) What angular momentum does the space station have?
b) If each of the rockets exerts a thrust of 125 N, for what time must the
rockets be fired to achieve the desired free fall acceleration?
Physics 1D03 - Lecture 31
Summary
In general, for a rigid body, L  r  ( mv CM )  I CM ω
In collisions, angular momentum will be conserved it there is
no external torque.
Physics 1D03 - Lecture 31