1. Angular Momentum III General motion of a rigid body + collisions
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Physics 1D03 - Lecture 31

2. Example 1
Comet Halley moves about the Sun in an elliptical orbit, which it’s closest approach to the sun being about 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

3. Example 2
Physics 1D03 - Lecture 31

4. 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

5. Example 4
Physics 1D03 - Lecture 31

6. Angular momentum” is the rotational analogue of linear momentum.
Recall:
Angular momentum” is the rotational analogue of linear momentum.
Hence, we should have a similar quantity to impulse in linear momentum (I = FΔt =Δp):
This ΔL is a ‘rotational impulse’.
Physics 1D03 - Lecture 31

7. Example 5
Physics 1D03 - Lecture 31

8. 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.
What angular momentum does the space station have?
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

9. Summary In general, for a rigid body,
In collisions, angular momentum will be conserved it there is no external torque.
Physics 1D03 - Lecture 31