1. Rotational Motion (rigid object about a fixed axis)
Chapter 10
Rotational Motion
(rigid object about
a fixed axis)

2. What is meant by a “rigid object”
What is meant by a “rigid object”? and a “rigid object about a fixed axis”?

3. Overview: Our approach
Introduction to thinking about rotation
Translational – Rotational motion analogy
Angular/Rotational quantities
constant angular acceleration motion
Torque and Rotational inertia
Rotational dynamics problem solving
Determining moments of inertial
Rotational Kinetic Energy
Energy Conservation
“Rolling friction” - comment

4. Introduction The goal Help along the way The Bonus
Describe rotational motion
Explain rotational motion
Help along the way
Analogy between translation and rotation
Separation of translation and rotation
The Bonus
Easier than it looks
Good review of translational motion
Encounter “modern” topics

5. Introduction The goal Just like translational motion
Describe rotational motion kinematics
Explain rotational motion dynamics
Help along the way
Analogy between translation and rotation
Separation of translation and rotation
The Bonus
Easier than it looks
Good review of translational motion
Encounter “modern” topics

6. Introduction The goal Help along the way A fairy tale The Bonus
Describe rotational motion
Explain rotational motion
Help along the way A fairy tale
Analogy between translation and rotation
Separation of translation and rotation
The Bonus
Easier than it looks
Good review of translational motion
Encounter “modern” topics

7. Introduction The goal Help along the way The Bonus A puzzle
Describe rotational motion
Explain rotational motion
Help along the way
Analogy between translation and rotation
Separation of translation and rotation
The Bonus A puzzle
Easier than it looks
Good review of translational motion
Encounter “modern” topics

8. A book is rotated through a point about a vertical axis by 900 and then through the same point in the book about a horizontal axis by If we start over and perform the same rotations in the reverse order, the orientation of the object:
1. will be the same as before.
2. will be different than before.
3. depends on the choice of point.

9. A book is rotated through a point about a vertical axis by 900 and then through the same point in the book about a horizontal axis by If we start over and perform the same rotations in the reverse order, the orientation of the object:
1. will be the same as before.
2. will be different than before.
3. depends on the choice of the point.
Some implications: Math, Quantum Mechanics … interesting!!!

10. Translational - Rotational Motion Analogy
What do we mean here by “analogy”?
Diagram of the analogy (on board)
Pair learning exercise on translational quantities and laws
Summation discussion on translational quantities and laws
Introduction of angular/rotational quantities
Formulation of the specific analogy
Validation of analogy

11. Translational - Rotational Motion Analogy (precisely)
If qti corresponds to qri for each translational and rotation quantity,
then L(qt1,qt2,…) is a translational dynamics formula or law, if and only if L(qr1,qr2,…) is a rotational dynamics formula or law.
(To the extent this is not true, the analogy is said to be limited. Most analogies are limited.)

12. Angular quantities Angle units: radians
Average and instantaneous quantities
Translational-angular connections
Example
Vector nature of angular quantities
Care needed (book rotation, other examples)
Tutorial on rotational motion (handout)

13. Constant angular acceleration
What is expected in analogy with the translational case?
And what is the mathematical and graphical representation for the case of constant angular acceleration?
Example (Physlet E10.2)

14. Torque Pushing over a block? Dynamic analogy with translational motion
When angular velocity is constant, what?...
What keeps a wheel turning?
Definition of torque magnitude
5-step procedure: 1.axis, 2.force and location, 3.line of force, 4.perpendicalar distance to axis, 5. torque = r┴ F
Question
Ranking tasks 101,93

15. Torque and Rotational Inertia
Moment of inertia
Derivation involving torque and Newton’s 2nd Law
Intuition from experience (demo: PVC rods)
Definition
Ranking tasks 99,100,98
…More later…

16. Rotational Dynamics Problem Solving
What are the lessons from translational dynamics?
Use of extended free body diagrams
For what purpose do simple free body diagrams still work very well?
Dealing with both translation and rotation
Examples
inc. Tutorial on Dynamics of Rigid Bodies

17. Questions
How could the moment of inertia of a particular object be determined?
What considerations are important to keep in mind?

18. Determining moment of inertia
By experiment
From mass density
Use of parallel-axis theorem
Use of perpendicular-axis theorem
Question
Ranking tasks 90,91,92

19. Rotational kinetic energy & the Energy Representation
Rotational work, kinetic energy, power
Conservation of Energy
Rotational kinetic energy as part of energy
question
Rolling motion
Rolling races
Jeopardy problems
Examples

20. “Rolling friction”
Optional topic
Worth a look, comments only

21. The end
Pay attention to the Summary of Rotational Motion.

22. A disk is rotating at a constant rate about a vertical axis through its center. Point Q is twice as far from the center of the disk as point P is. Draw a picture. The angular velocity of Q at a given time is:
twice as big as P’s.
the same as P’s.
half as big as P’s.
None of the above.
back

23. When a disk rotates counterclockwise at a constant rate about the vertical axis through its center (Draw a picture.), the tangential acceleration of a point on the rim is:
positive.
zero.
negative.
not enough information to say.
back

24. A wheel rolls without slipping along a horizontal surface
A wheel rolls without slipping along a horizontal surface. The center of the wheel has a translational speed v. Draw a picture. The lowermost point on the wheel has a net forward velocity: 2v v
zero
not enough information to say
back

25. The moment of inertia of a rigid body about a fixed axis through its center of mass is I. Draw a picture. The moment of inertia of this same body about a parallel axis through some other point is always:
smaller than I.
the same as I.
larger than I.
could be either way depending on the choice of axis or the shape of the object.
back

26. A ball rolls (without slipping) down a long ramp which heads vertically up in a short distance like an extreme (and dysfunctional) ski jump. The ball leaves the ramp straight up. Refer to picture. Assume no air drag and no mechanical energy is lost, the ball will:
reach the original height.
exceed the original height.
not make the original height.
back

27. (5kg)(9.8m/s2)(10m) = (1/2)(5kg)(v)2 + (1/2)(2/5)(5kg)(.1m)2(v/(.1m))2
Draw a picture and label relevant quantities.
back

28. (5kg)(9.8m/s2)(10m) = (1/2)(5kg)(v)2 + (1/2)(2/5)(5kg)(.1m)2(v/(.1m))2
(5kg)(9.8m/s2)(h) = (1/2)(5kg)(v)2
Draw a picture and label relevant quantities.
back

29. (1/2)(5kg)(.1m/s)2 + (1/2)(1/2)(5kg)(.2m)2(.1m/s/(.1m))2
= (1/2)(5kg)(v)2 + (1/2)(1/2)(5kg)(.2m)2(v/(.2m))2
Draw a picture and label relevant quantities.
back

30. Suppose you pull up on the end of a board initially flat and hinged to a horizontal surface.
How does the amount of force needed change as the board rotates up making an angle Θ with the horizontal?
a. Decreases with Θ
b. Increases with Θ
c. Remains constant
back

31. Several solid spheres of different radii, densities and masses roll down an incline starting at rest at the same height.
In general, how do their motions compare as they go down the incline, assuming no air resistance or “rolling friction”?
Make mathematical arguments on the white boards.
back

32. (1kg)(9.8m/s2)(1m)
= (1/2)(1/2)(.25kg)(.05m)2(v/.05m)2
+ (1/2)(1kg)v2
Draw a picture and label relevant quantities.
back

33. Consider a board set up between on two scales that measure the force on them. And suppose the distance between the scales is L and the weight of the board is wB.
What weight does each scale read?
If an object of weight w is put on the board a distance d from scale on the right, what will the right and left scales read?
back