1. Physics 218 Lecture 18
Dr. David Toback
Physics 218, Lecture XVIII

2. Announcements Chapter 9 HW due Wed Nov 8th
Chapter 10 HW due Monday Nov 13th, as usual
First Announcement of Exam 3:
November 21st
Tuesday before Thanksgiving!
Physics 218, Lecture XVIII

3. Rotational Motion Chapters 9 and 10 in four lectures
Lecture three of the four lectures
Concentrate on the relationship between linear and angular variables
Today: Finish up topics
Thursday: Hard problems
Physics 218, Lecture XVIII

4. Physics 218, Lecture XVIII

5. Angular Quantities Position  Angle q Velocity  Angular Velocity w
Acceleration  Angular Acceleration a
Force  Torque t
Mass  Moment of Inertia I
Today we’ll finish:
Momentum
Energy
Physics 218, Lecture XVIII

6. Momentum Momentum vs. Angular Momentum: Newton’s Laws:
Physics 218, Lecture XVIII

7. Angular Momentum First way to define the Angular Momentum L:
Physics 218, Lecture XVIII

8. Angular Momentum Definition
Another definition:
Physics 218, Lecture XVIII

9. Angular Motion of a Particle
Determine the angular momentum, L, of a particle, with mass m and speed v, moving in circular motion with radius r
Physics 218, Lecture XVIII

10. Conservation of Angular Momentum
By Newton’s laws, the angular momentum of a body can change, but the angular momentum for a system cannot change
Conservation of Angular Momentum
Same as for linear momentum
Physics 218, Lecture XVIII

11. Ice Skater This one you’ve seen on TV
Try this at home in a chair that rotates
Get yourself spinning with your arms and legs stretched out, then pull them in
Physics 218, Lecture XVIII

12. BEFORE and AFTER Problem Solving
For Conservation of Angular Momentum problems:
BEFORE and AFTER
Physics 218, Lecture XVIII

13. Conservation of Angular Momentum
Before
Physics 218, Lecture XVIII

14. Conservation of Angular Momentum
After
Physics 218, Lecture XVIII

15. Clutch Design
As a car engineer, you model a car clutch as two plates, each with radius R, and masses MA and MB (IPlate = ½MR2). Plate A spins with speed w1 and plate B is at rest. you close them so they spin together
Find the final angular velocity of the system
Physics 218, Lecture XVIII

16. Angular Quantities Position  Angle q Velocity  Angular Velocity w
Acceleration  Angular Acceleration a
Force  Torque t
Mass  Moment of Inertia I
Today we’ll finish:
Momentum  Angular Momentum L
Energy
Physics 218, Lecture XVIII

17. Rotational Kinetic Energy
KEtrans = ½mv2
 KErotate = ½Iw2
Conservation of Energy must take rotational kinetic energy into account
Physics 218, Lecture XVIII

18. Rotation and Translation
Objects can both Rotate and Translate
Need to add the two
KEtotal = ½ mv2 + ½Iw2
Rolling without slipping is a special case where you can relate the two
V = wr
Physics 218, Lecture XVIII

19. Rolling Down an Incline
You take a solid ball of mass m and radius R and hold it at rest on a plane with height Z. You then let go and the ball rolls without slipping.
What will be the speed of the ball at the bottom?
What would be the speed if the ball didn’t roll and there were no friction?
Note:
Isphere = 2/5MR2 Z
Physics 218, Lecture XVIII

20. A bullet strikes a cylinder
A bullet of speed V and mass m strikes a solid cylinder of mass M and inertia I=½MR2, at radius R and sticks. The cylinder is anchored at point 0 and is initially at rest.
What is w of the system after the collision?
Is energy Conserved?
Physics 218, Lecture XVIII

21. 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 w when it reaches the bottom?
What is the velocity of the tip at the bottom?
Physics 218, Lecture XVIII

22. Less Spherical Heavy Pulley
A heavy pulley, with radius R, starts at rest. We pull on an attached rope with constant force FT. It accelerates to final angular speed w in time t.
A better estimate takes into account that there is friction in the system. This gives a torque (due to the axel) we’ll call this tfric.
What is this better estimate of the moment of Inertia? R
Physics 218, Lecture XVIII

23. Person on a Disk
A person with mass m stands on the edge of a disk with radius R and moment ½MR2. Neither is moving.
The person then starts moving on the disk with speed V.
Find the angular velocity of the disk
Physics 218, Lecture XVIII

24. Same Problem: Forces Same problem but with Forces
Physics 218, Lecture XVIII

25. Next Time Please get caught up on homework!!!
More problems on Chapters 9 & 10
Please get caught up on homework!!!
Believe it or not exam 3 is just around the bend, Nov 21st
Tuesday before Thanksgiving!
Chap 9 HW due Wednesday Nov 8th
Chap 10 HW due Nov 13th
Physics 218, Lecture XVIII

26. End of Lecture Notes
Physics 218, Lecture XVIII

27. Exam II Mean = 75 Average on first two exam = 76%
Please check to make sure they added your points correctly AND entered them into WebCT correctly!!!
Average on first two exam = 76%
Straight scale so far…
Reading quizzes should be passed back in recitation
Physics 218, Lecture XVIII

28. Next Time Reading Questions: Q11.X & Q11.X XXX FIXME!!!
Chapter 11
Reading Questions: Q11.X & Q11.X
XXX FIXME!!!
Math, Torque, Angular Momentum, Energy again, but more sophisticated
The material will not be on the 3rd exam, but will help with the exam. It will all be on the final
HW 10 Due Monday
Exam 3 is next Thursday, April 22nd
Physics 218, Lecture XVIII

29. Angular Quantities Position  Angle q Velocity  Angular Velocity w
Acceleration  Angular Acceleration a
Force  Torque t
Today we’ll finish:
Mass
Momentum
Energy
Physics 218, Lecture XVIII

30. Calculating Moments of Inertia
Here r is the distance from the axis of each little piece of mass
Physics 218, Lecture XVIII

31. Calculate the Moment of Inertia
A pulley has mass M, uniform density, radius R, and rotates around its fixed axis
Calculate its moment of inertia R
Physics 218, Lecture XVIII

32. Calculate the Moment of Inertia
Better example here…
Calculate its moment of inertia R
Physics 218, Lecture XVIII

33. Physics 218, Lecture XVIII

34. Hollow Cylinder
Consider a hollow cylinder with uniform density, inner radius R1, outer radius R2 and total Mass M.
Find the moment of Inertia
Physics 218, Lecture XVIII

35. Parallel-Axis Theorem
Quick Trick for calculating Moments
I = Icm + Mh2
Example
Physics 218, Lecture XVIII