Lecture 4 of 25 Review HW problem 1

Lecture #4 of 25 Review HW problem 1. 9 Explain 3 in-class problems from Tuesday Angular Momentum n n And torque And Central force Moment of Inertia – Worked example DVD Demonstration on momentum cons. and CM motion 1 : 10

Impulse II -- Problem #L 2 -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 seatbelts. 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 2 : 20 average force for each? How many “g’s” do they feel.

Worked Example L 3 -1 – 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 3 : 30

Worked Example L 3 -2 – Continuous mass 2 km Given quarter circle 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, both r and phi components Solve integral Calculate Given origin O 1 4 : 40

Equivalence of Linear and Angular motion equations 5 : 45

Moment of Inertia vs. Center of Mass For a multi-particle discrete mass-distribution For a continuous mass-distribution . 6 : 45

Angular Momentum and Torque 7 : 50

Parallel Axis Theorem d Axis 2 (Parallel to axis 1) CM Axis 1 (through CM) 8 : 55

Angular Momentum and Central Forces 9 : 45

Moment of Inertia worked problem w 2 L w 1 Calculate the moment of inertia and kinetic energy of a wire of uniform mass-density lambda, mass M, and length L. n A) If rotated about axis at midpoint at angular w n velocity 1 B) If rotated about axis at endpoint at angular velocity w 2 10 : 60

Lecture #4 Wind-up. . . We are done w/ chapters 1 and 3, read all. Assignment includes Taylor /Supplement / Lecture probs. 11 : 72