Lecture 3 Center of Mass n n Defined

Lecture #3 Center of Mass n n Defined Relation to momentum Polar, Cylindrical and Spherical Coordinates Worked problems DVD Demonstration on momentum cons. and CM motion 1 : 10

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

Worked Example L 3 -1 – CM Motion Initial Final Given m 1 to m 2 m= m Initial Final m = 3 m Calculate Vcm Initial and Final for two cases 3 : 50

Linear Momentum and CM 4 : 20

Spherical Coordinates and Earth Spherical coordinates “Phi” or “Fee” (j) – Eastwest same as longitude n “Theta” (q) – North-south, same as Colatitude n w(q) is 0 at north pole, 180 at south pole, 90 at equator n “r” (radius) 5 : 60

Cylindrical and Spherical Coordinates Coord. System Area d. A Volume d. V Cartesian Spherical Cylindrical Polar 6 : 30

Worked Example L 3 -2 – Discrete masses 2 units Given m 1 to m 10 y O 2 y x O 1 x 1 unit m a= m ma = 3 m Calculate Given origin O 1 For homework given O 2 7 : 50

Worked Example L 3 -3 – Continuous mass 2 km Given quarter disk with uniform mass-density s and radius 2 km: j O 1 r n n Calculate M total Write r in polar coords Write out double integral, in r and phi Solve integral Calculate Given origin O 1 • REPEAT for Half disk 8 : 60

Lecture #3 Wind-up. . . Office hours today and tomorrow 4 -5: 30. Homework problems in Taylor, + Supplement. Second homework due in class Thursday 9/4 9 : 72