1. Gyroscopes Lecturer: Professor Stephen T. Thornton

2. Reading Quiz The position vector from the axis to where a force is applied to a wheel is and the force vector is In what direction is the torque? A) B) C) D) E)

3. Answer: E

4. Last Time Angular momentum and torque system of particles
rigid objects
Unbalanced torque
Kepler’s 2nd law

5. Today Angular momentum and torque Gyroscopes
Inertial forces, pseudoforces
Review

6. Struck Think Rod. A thin rod of mass M and length rests on a frictionless table and is struck at a point from its CM by a clay ball of mass m moving at speed v. The ball sticks to the rod. Determine the translational and rotational motion of the rod after the collision.
Giancoli, 4th ed, Problem 11-51

7. The Right-Hand Rule for Torque

8. Torque and Angular Momentum Vectors

9. The Torque Exerted on a Gyroscope
Do demo.

10. Precession of a Gyroscope

11. The Spinning Top and Gyroscope
A spinning top will precess around its point of contact with a surface, due to the torque created by gravity when its axis of rotation is not vertical.
Do the frictionless demo and use drill to spin top. Make sure I spin it in the way shown here. Also try to spin a spinning top. Note that a right hander will spin it in the opposite direction as shown here.

12. The Spinning Top and Gyroscope
The angular velocity of the precession is given by:
This is also the angular velocity of precession of a toy gyroscope, as shown previously.

13. Uses of Gyroscopes
Navigation has largely been superseded by GPS, but still useful for stabilizers
Satellites – example is Hubble Space Telescope
Virtual Reality helmets – used to discern person’s motion
Racing cars – engine is a gyroscope
Bicycles and motor bikes
Robot orientation
See for some descriptions.

14. Rotating Frames of Reference; Inertial Forces
An inertial frame of reference is one in which Newton’s laws hold; a rotating frame of reference is noninertial, and objects viewed from such a frame may move without a force acting on them.
Figure Path of a ball released on a rotating merry-go-round (a) in the reference frame of the merry-go-round, and (b) in a reference frame fixed on the ground.

15. Rotating Frames of Reference; Inertial Forces
There is an apparent outward force on objects in rotating reference frames; this is a fictitious force, or a pseudo force. The centrifugal “force” is of this type; there is no outward force when viewed from an inertial reference frame.

16. Show two videos Skateboard aerials Figure skater
These two flash videos are on my Home directory. Both are good. The figure skater video is 2:30 long, discusses torque, etc. Skateboard aerial is 3 min.

17. Rolling Tire. A boy rolls a tire along a straight level street
Rolling Tire. A boy rolls a tire along a straight level street. The tire has mass 8.0 kg, radius 0.32 m and moment of inertia about its central axis of symmetry of 0.83 kg m2. The boy pushes the tire forward away from him at a speed of 2.1 m/s and sees that the tire leans 12° to the right. (a) How will the resultant torque affect the subsequent motion of the tire? (b) Compare the change in angular momentum caused by this torque in 0.20 s to the original magnitude of angular momentum.
Giancoli, 4th ed, Problem 11-71

18. Conceptual Quiz A student sits on a spinning stool with her arms folded. When she extends her arms away from her body, her kinetic energy
Increases
Decreases
Stays the same
Depends on her mass
Need further information

19. Conceptual Quiz
Decreases
Angular momentum is conserved. Rotational inertia is increased.
How is this possible? What happened to the energy? Is conservation of energy violated?
increases

20. Conceptual Quiz A student sits on a spinning stool with her arms folded. When she extends her arms away from her body, her kinetic energy
B) Decreases Why? Some of the kinetic energy is converted to potential energy, because her arms are extended!

21. Conceptual Quiz The name of the quantity which is greater for a long 70 kg barbell than for a short 75 kg barbell that makes it harder for us to hold and twist it is called rotational
kinetic energy
momentum
inertia
mass
center of mass

22. Conceptual Quiz The name of the quantity which is greater for a long 70 kg barbell than for a short 75 kg barbell that makes it harder to twist is called rotational
C) inertia

23. Conceptual Quiz A wheel of outer radius R has an axle of radius R/6
Conceptual Quiz A wheel of outer radius R has an axle of radius R/6. Strings are wrapped as shown around the rim of the wheel and around the axle. If the string around the rim of the wheel has tension T, what must be the tension T’ in the string around the axle in order for the wheel to not move? T’

24. Answer: A) 6T We want torque = 0

25. Dropping Disk. A nonrotating cylindrical disk of moment of inertia I is dropped onto an identical disk rotating at angular speed ω. Assuming no external torques, what is the final common angular speed of the two disks?
Giancoli, 4th ed, Problem 11-15