PHYS 220 General Physics II 12 FEB 2018 PHYS 220 General Physics II Today: Base Groups Angular momentum Rolling motion Oscillations

Science Seminar hosted by Natural and Health Sciences Join us for the first Science Seminar of the Spring Semester! Everyone is welcome! Topic… Just Think: Four Lessons from Math Presenter… Dr. Andy Rich Manchester University Professor of Mathematics February 12, 2018 Math & Computer Science 4:00 – 5:00 PM Flory Auditorium (SCIC 203) Snacks provided

Base Group Meeting BGDG: What does your favorite breakfast look like? Base Group WorkSheet Group Processing Reading Quiz

Reading Quiz 02 1. The SI unit of charge is the __A. Ampère __B. Volt __C. Newton __D. Coulomb 2. A proton has the smallest unit of charge, 1.6 x 10-19 C. All charged objects will have a total charge equal to some multiple of this unit. This is an illustration of ___A. the conservation of charge. ___C. the quantization of charge. ___B. ionization energy. ___D. Coulomb’s law. 3. Like charges repel and unlike charges attract. The force of attraction/repulsion depends on the magnitude of the charges and the distance between them. This is summarized in ___A. the conservation of charge. ___C. the quantization of charge. ___B. the triboelectric effect. ___D. Coulomb’s law. 4. For a damped simple harmonic oscillator which of the following is true? ___ A. Mechanical energy is conserved. ___ B. Mechanical energy is converted into thermal energy. ___ C. Total energy is not conserved. ___ D. Mechanical energy is served, with a light crème sauce.

Angular momentum Which, in the absence of external torques, Where else do we see a cross product? Units? kgm2/s Which, in the absence of external torques, is a conserved quantity!

For a system of particles So that (for constant I ) Angular momentum For a system of particles and for rigid bodies So that (for constant I )

Conservation of Angular Momentum For a system with no external torques, the angular momentum of the system is a constant: If then

EX: Conservation of Angular Momentum A clay bullet of mass mb and speed vb is fired at a cylinder of mass M and radius R (initially at rest) with an “impact parameter” b. Find the angular velocity of the system after the bullet sticks to the outer surface of the cylinder b solid cylinder: I = ½ M R2 R

The Work-Energy Theorem Should look familiar! Wnet=work done by the net torque

Rolling without Slipping Axle moves at speed vcom Distance traveled by axle, s, is related to the angle the wheel rotates through by s = R θ, R = wheel radius Vcom = ω R (no slipping) The wheel needs friction to roll!

Kinetic energy of rolling Recall: Vcom = ω R

Rolling Motion Cylinders of different I rolling down an inclined plane: DK = - DU = Mgh v = 0 w = 0 K = 0 R M h

Join us for the first Science Seminar of the Seminar day! GO! Join us for the first Science Seminar of the Spring Semester! Everyone is welcome! Topic… Just Think: Four Lessons from Math Presenter… Dr. Andy Rich Manchester University Professor of Mathematics