1. Physics 218, Lecture XIX1 Physics 218 Lecture 19 Dr. David Toback

2. Physics 218, Lecture XIX2 Rotational Motion Last lecture on Chapters 9 & 10 –We’ll work on hard problems to try and cover the main topics –Will use these topics for Chap 11: Statics Exam 3 –Coming up soon: November 21 st –Tuesday before Thanksgiving –Covers Chapters 8-11

3. Physics 218, Lecture XIX3

4. 4 A bullet strikes a cylinder A bullet of speed V and mass m strikes a solid cylinder of mass M and moment of inertia I=½MR 2, at radius R and sticks. The cylinder is anchored at point 0 and is initially at rest What is  of the system after the collision?

5. Physics 218, Lecture XIX5 Rolling Down an Incline A solid ball of mass m and radius R starts from rest and rolls without slipping down a plane with height Z. Using forces, what will be the final speed of the ball? Note: I sphere = 2/5MR 2 Z

6. Physics 218, Lecture XIX6 Rotating Rod A rod of mass uniform density, mass m and length l pivots at a hinge. It has moment of inertia I=ml/3 and starts at rest at a right angle. You let it go: What is  when it reaches the bottom? What is the velocity of the tip at the bottom?

7. Physics 218, Lecture XIX7 Person on a Disk A person with mass m stands on the edge of a disk with radius R and moment ½MR 2. Neither is moving. The person then starts moving on the disk with speed V. Find the angular velocity of the disk

8. Physics 218, Lecture XIX8 Less Spherical Heavy Pulley A heavy pulley, with radius R, starts at rest. We pull on an attached rope with constant force F T. It accelerates to final angular speed  in time t. We note that there is friction in the system. This gives a torque (due to the axel) we’ll call this  fric. What is the moment of Inertia? R

9. Physics 218, Lecture XIX9 Next Week Chapter 11 (Statics) and 12 (Gravity) –No reading questions… If I think people haven’t done the reading I’ll just give an in-class quiz –Statics will be on exam 3 (last topic) Please get caught up on the homework!!! –HW10 due on Monday Exam 3 is November 21 st –Tuesday before Thanksgiving!

10. Physics 218, Lecture XIX10

11. Physics 218, Lecture XIX11 A bullet strikes a cylinder A bullet of speed V and mass m strikes a solid cylinder of mass M and moment of inertia I=½MR 2, at radius R and sticks. The cylinder is anchored at point 0 and is initially at rest What is  of the system after the collision? Is energy Conserved?

12. Physics 218, Lecture XIX12 Kepler’s 2 nd Law 2 nd Law: Each planet moves so that an imaginary line drawn from the Sun to the planet sweeps out area in equal periods of time

13. Physics 218, Lecture XIX13 Atwood’s Machine A pulley with a fixed center (at point O), radius R  and moment of inertia I, has a massless rope wrapped around it (no slipping). The rope has two masses, m 1 and m 2 attached to its ends. Assume m 2 >m 1 What is the acceleration of the system? Do some checks.

14. Physics 218, Lecture XIX14 Same Problem: Forces Same problem but with Forces

15. Physics 218, Lecture XIX15 Next Period: Exam 3 Review Exam: –Problems similar to those from the Textbook, Homework and Lecture –Formula sheet handed out –All formulas you use must be derived from those on the formula sheet Topics are: Chapters 8-10 –Conservation of Energy –Momentum and Collisions –Rotational Motion notToday’s Topics not covered, but are a review

16. Physics 218, Lecture XIX16 Extra Credit For exam 3, there are now a possible 5 extra credit points available to you if you complete the following before the exam: 1.Have a 100 on all HW and HWq up to, and including, CH10 as well as the math quizzes. 2.When you do, a mini-practice exam will become available to you. 3.You can take as many mini-practice exams as you like until you get a 100 4.If you get a 100, you will get 5 extra credit points

17. Physics 218, Lecture XIX17 Why does the Bicycle Wheel Turn to the Right?

18. Physics 218, Lecture XIX18 Angular Momentum Again we use the Cross Product: Derivation of  = dL/dt

19. Physics 218, Lecture XIX19 L for a system of many bodies Have to be careful with Angular Momentum –  = dl/dt for a single particle –  =  dl/dt) for a system of many particles –All internal torques cancel because of Newton’s law (all internal forces are equal and opposite) Reference Frame matters. Only true for: –The origin is an inertial Reference Frame –The center of mass

20. Physics 218, Lecture XIX20 L for a Rigid Body Find the angular momentum, L, for this body given that it is rotating around the Z axis with angular velocity 