1. PHY 231 1 PHYSICS 231 Lecture 20: Angular momentum Remco Zegers Walk-in hour: Thursday 11:30-13:30 am Helproom Neutron star

2. PHY 231 2 In the previous episode..  =I  (compare to  F=ma ) Moment of inertia I: I=(  m i r i 2 )  : angular acceleration I depends on the choice of rotation axis!!

3. PHY 231 3 Rotational kinetic energy KE r =½I  2 Conservation of energy for rotating object: [PE+KE t +KE r ] initial = [PE+KE t +KE r ] final Example. 1m

4. PHY 231 4 Angular momentum Conservation of angular momentum If the net torque equal zero, the angular momentum L does not change I i  i =I f  f

5. PHY 231 5 Conservation laws: In a closed system: Conservation of energy E Conservation of linear momentum p Conservation of angular momentum L

6. PHY 231 6 Neutron star Sun: radius: 7*10 5 km Supernova explosion Neutron star: radius: 10 km I sphere =2/5MR 2 (assume no mass is lost)  sun =2  /(25 days)=2.9*10 -6 rad/s Conservation of angular momentum: I sun  sun =I ns  ns (7E+05) 2 *2.9E-06=(10) 2 *  ns  ns =1.4E+04 rad/s so period T ns =5.4E-04 s !!!!!!

7. PHY 231 7 The spinning lecturer… A lecturer (60 kg) is rotating on a platform with  =2  rad/s (1 rev/s). He is holding two masses of 0.8 m away from his body. He then puts the masses close to his body (R=0.0 m). Estimate how fast he will rotate.

8. PHY 231 8 ‘2001 a space odyssey’ revisited (lec. 16, sh. 12) A spaceship has a radius of 100m and I=5.00E+8 kgm 2. 150 people (65 kg pp) live on the rim and the ship rotates such that they feel a ‘gravitational’ force of g. If the crew moves to the center of the ship and only the captain would stay behind, what ‘gravity’ would he feel?

9. PHY 231 9 The direction of the rotation axis The conservation of angular momentum not only holds for the magnitude of the angular momentum, but also for its direction. The rotation in the horizontal plane is reduced to zero: There must have been a large net torque to accomplish this! (this is why you can ride a bike safely; a wheel wants to keep turning in the same direction.) L L

10. PHY 231 10 Rotating a bike wheel! LL A person on a platform that can freely rotate is holding a spinning wheel and then turns the wheel around. What will happen?

11. PHY 231 11 Demo: defying gravity!

12. PHY 231 12 Global warming The polar ice caps contain 2.3x10 19 kg of ice. If it were all to melt, by how much would the length of a day change? M earth =6x10 24 kg R earth =6.4x10 6 m

13. PHY 231 13 Two for the weekend... 12.5N 30N What is the tension in the tendon?

14. PHY 231 14 A top A top has I=4.00x10 -4 kgm 2. By pulling a rope with constant tension F=5.57 N, it starts to rotate along the axis AA’. What is the angular velocity of the top after the string has been pulled 0.8 m?