1. Physics 101: Lecture 19, Pg 1 Physics 101: Lecture 19 Rotational Dynamics l Today’s lecture will cover Textbook Chapter 9 è Concept Questions and Example Problems è More on Angular Momentum and Conservation of Angular Momentum

2. Physics 101: Lecture 19, Pg 2 See text: chapters 8-9 See Table 8.1 Angular Momentum MomentumAngular Momentum p = m v L = I  conserved if  F ext = 0conserved if  ext =0 VectorVector! units: kg m/sunits: kg m 2 /s

3. Physics 101: Lecture 19, Pg 3 Concept Question You are sitting on a freely rotating bar-stool with your arms stretched out and a heavy glass mug in each hand. Your friend gives you a twist and you start rotating around a vertical axis though the center of the stool. You can assume that the bearing the stool turns on is frictionless, and that there is no net external torque present once you have started spinning. You now pull your arms and hands (and mugs) close to your body.

4. Physics 101: Lecture 19, Pg 4 Concept Question What happens to your angular momentum as you pull in your arms? 1. it increases 2. it decreases 3. it stays the same L1L1 L2L2 This is like the spinning skater example in the book. Since the net external torque is zero (the movement of the arms and hands involve internal torques), the angular momentum does not change. CORRECT

5. Physics 101: Lecture 19, Pg 5 Concept Question 11 22 I2I2 I1I1 L L What happens to your angular velocity as you pull in your arms? 1. it increases 2. it decreases 3. it stays the same as with the skater example given in the book....as you pull your arms in toward the rotational axis, the moment of inertia decreases, and the angular velocity increases. CORRECT

6. Physics 101: Lecture 19, Pg 6 Concept question What happens to your kinetic energy as you pull in your arms? 1. it increases 2. it decreases 3. it stays the same CORRECT Your angular velocity increases and moment of inertia decreases, but angular velocity is squared, so KE will increase with increasing angular velocity 11 22 I2I2 I1I1 L L (using L = I  )

7. Physics 101: Lecture 19, Pg 7 l Two different spinning disks have the same angular momentum, but disk 2 has a larger moment of inertia than disk 1. è Which one has the biggest kinetic energy ? (a) disk 1 (b) disk 2 Spinning disks

8. Physics 101: Lecture 19, Pg 8 If they have the same L, the one with the smallest I will have the biggest kinetic energy.  disk 2  disk 1 I 1 < I 2 (using L = I  )

9. Physics 101: Lecture 19, Pg 9 Preflights 7 & 8: Turning the bike wheel A student sits on a barstool holding a bike wheel. The wheel is initially spinning CCW in the horizontal plane (as viewed from above). She now turns the bike wheel over. What happens? 1. She starts to spin CCW. 2. She starts to spin CW. 3. Nothing CORRECT

10. Physics 101: Lecture 19, Pg 10 Turning the bike wheel... l Since there is no net external torque acting on the student- stool system, angular momentum is conserved. è Remenber, L has a direction as well as a magnitude! LL Initially: L INI = L W,I LLL Finally: L FIN = L W,F + L S L L W,F LLSLLS L L W,I LLL L W,I = L W,F + L S