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Physics 101: Lecture 19 Rotational Dynamics

Physics 101: Lecture 19 Rotational Dynamics. Today’s lecture will cover Textbook Chapter 9 Concept Questions and Example Problems More on Angular Momentum and Conservation of Angular Momentum. See text: chapters 8-9. Angular Momentum. Momentum Angular Momentum p = m v L = I 

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Physics 101: Lecture 19 Rotational Dynamics

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

  2. See text: chapters 8-9 Angular Momentum Momentum Angular Momentum p = m vL = I  conserved if Fext = 0conserved if ext =0 Vector Vector! units: kg m/s units: kg m2/s See Table 8.1

  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. CORRECT L1 L2 Concept Question What happens to your angular momentum as you pull in your arms? 1. it increases2. it decreases3. it stays the same 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.

  5. CORRECT w2 w1 I2 I1 L L Concept Question What happens to your angular velocity as you pull in your arms? 1. it increases2. it decreases3. 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.

  6. (using L = I ) CORRECT w2 w1 I2 I1 L L Concept question What happens to your kinetic energy as you pull in your arms? 1. it increases2. it decreases3. it stays the same Your angular velocity increases and moment of inertia decreases, but angular velocity is squared, so KE will increase with increasing angular velocity

  7. Spinning disks • Two different spinning disks have the same angular momentum, but disk 2 has a larger moment of inertia than disk 1. • Which one has the biggest kinetic energy ? (a) disk 1 (b) disk 2

  8. (using L = I ) If they have the same L, the one with the smallestIwill have the biggest kinetic energy. w1 w2 I1 < I2 disk 1 disk 2

  9. CORRECT 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

  10. Turning the bike wheel... • Since there is no net external torque acting on the student-stool system, angular momentum is conserved. • Remenber,Lhas a direction as well as a magnitude! Initially: LINI= LW,I Finally: LFIN= LW,F+LS LS LW,I LW,I = LW,F+LS LW,F

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