1 Lecture #3 of 25 Homework #1 expectations Questions on Assignment #2 Center of Mass Defined Relation to momentum Polar and Spherical Coordinates Worked problems DVD Demonstration on momentum cons. and CM motion :10

2 Center of Mass Center of Mass and Center of gravity happen to be equivalent For a multi-particle discrete mass-distribution For a continuous mass-distribution. :15

3 Linear Momentum and CM :20

4 Spherical Coordinates and Earth Radius on surface of earth is fixed, so two coordinates are sufficient to specify any point on Earth Coordinates are: Latitude (North-south)  “Co-latitude” is 90 degrees minus latitude Longitude (East-West) Spherical coordinates “Phi” or “Fee”  – East-west same as longitude “Theta”  – North-south, same as Colatitude   is 0 at north pole, 180 at south pole, 90 at equator For third dimension, add “r” (radius) :25

5 Cylindrical and Spherical Coordinates :30

6 Impulse II -- Problem #L2-3 “Another car crash” James and Joan are partly recovered from their previous injuries, and haven’t learned from their experience. They are drinking Jack Daniels and not wearing seat- belts. James’ vehicle has velocity vector Joan’s vehicle has Both vehicles’ mass=M. Both people’s mass=70 kg. Solve for case of inelastic and elastic collisions of vehicles. Joan has an airbag in her vehicle. It takes her 100 millisec to reduce her velocity relative to her vehicle to zero. James stops 5 millisec after impacting the steering wheel. What impulse does each person experience? What is average force for each? How many “g’s” do they feel. :40

7 Worked Example L3-1 – Discrete masses Given m 1 to m 10 m  = m m  = 3m y x y x O1O1 O2O2 1 unit 2 units Calculate Given origin O1O1 For homework given O 2 :50

8 Worked Example L3-2 – Continuous mass Given quarter circle with uniform mass-density  and radius 2 km: Calculate M total Write r in polar coords Write out double integral, both r and phi components Solve integral  r O1O1 2 km Calculate Given origin O1O1 :60

9 Lecture #3 Wind-up. Office hours Today 2:30-4, tomorrow 4-5:30. Homework problems in Taylor, Handout, Galileo problem – check the web. Second homework due in class Thursday 9/5 :72