1 / 46

Re-evaluation Request Due Quiz 2 May 22 (next Thursday) Quiz 3 May 29

Physics 7B - AB Lecture 7 May 15 Recap Angular Momentum Model (Second half of Chap 7) Recap Torque, Angular Momentum Rotational Inertia (new concept!) Intro to Newtonian Model (start Chapter 8). Re-evaluation Request Due Quiz 2 May 22 (next Thursday) Quiz 3 May 29. Quiz 3 average 7.75 (C+).

callum-gill
Download Presentation

Re-evaluation Request Due Quiz 2 May 22 (next Thursday) Quiz 3 May 29

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Physics 7B - ABLecture 7May 15Recap Angular Momentum Model (Second half of Chap 7)Recap Torque, Angular MomentumRotational Inertia (new concept!) Intro to Newtonian Model (start Chapter 8)

  2. Re-evaluation Request Due Quiz 2 May 22 (next Thursday)Quiz 3 May 29 Quiz 3 average 7.75 (C+) Quiz 4 graded, solution up on the web, rubrics will follow

  3. Recap Rotational (Angular) Motion gentleman bugis Ladybug Gentlemanbug

  4. Recap Rotational (Angular) Motion gentleman bugis Ladybug Gentlemanbug B) The two bugs each travel the same angle (ie. one revolution or 2p radians or any other angle) in the same amount of time so they have the same angular velocity

  5. Recap Rotational (Angular) Motion  ladybugpoints along the Ladybug

  6. Recap Rotational (Angular) Motion  ladybugpoints along the Ladybug E) Use your right hand to show that the angular velocity points along the +z axis.

  7. Recap Rotational (Angular) Motion the pivot point. F What is the direction of this torque ? Torque vector  pointing into the slide (clockwise rotation) Torque vector  pointing out of the slide (counterclockwise rotation) Torque is zero.

  8. Recap Rotational (Angular) Motion the pivot point. F What is the direction of this torque ? Torque vector  pointing into the slide (clockwise rotation) Torque vector  pointing out of the slide (counterclockwise rotation) Torque is zero. B) You should see that pushing this way will tend to rotate the wheel counterclockwise about its axle and that the right hand rule give you a torque vector pointing toward you.

  9. Recap Rotational (Angular) Motion vtablecloth FEarth on the goblet F/ /table cloth on the goblet (friction) F table cloth on the goblet

  10. Recap Rotational (Angular) Motion vtablecloth FEarth on the goblet F/ /table cloth on the goblet (friction) F table cloth on the goblet B) Very similar to the previous question. If the goblet tips over, it will tip over counterclockwise.

  11. Torque - rotational force that can change the rotational motion Force is exerted tangentially on the rim, the rim is at a distance r (moment arm) from the pivot point. Ftangential r Direction of  is given by the RHR Direction of Torque Force and Torque are two different physical quantities! Torque this way Rotation this way

  12. Rotational motion is changed by applying forces, But where the force is applied is Just as important as the size of the force Ftangential r Magnitude of Torque  = rFtangential = r Ftangential Force and Torque are two different physical quantities!

  13. Recap Extended Force Diagram Fstring on Plank

  14. Recap Extended Force Diagram Fstring on Plank

  15. Recap Extended Force Diagram Ffulcrum on Plank

  16. Recap Extended Force Diagram Ffulcrum on Plank

  17. Recap Extended Force Diagram FEarth on Plank

  18. Recap Extended Force Diagram FEarth on Plank

  19. Recap Rotational (Angular) Motion

  20. Ffulcrum on Plank F ?? Fstring on Plank = – (M/2)g FEarth on Plank = – Mg

  21. Angular analogue to Impulse is Angular Impulse • Angular Impulse Is related to the net external torque in the following way: Net Angular Impulseext = ∆ L = ∫ext(t)dt If the torque is constant during a time interval ∆t Net Angular Impulseext = ∆ L = ave.ext x ∆ t If the net torque is zero, the plank will stay stationary…

  22. Ffulcrum on Plank F Fstring on Plank = – (M/2)g FEarth on Plank = – Mg

  23. Ffulcrum on Plank F = (M/6)g Fstring on Plank = – (M/2)g FEarth on Plank = – Mg ave.ext= (L/4)(M/2)g+ (0)(M/2)g– (L/4)Mg+ (3L/4) F = 0 (L/4)(M/2)g– (L/4)Mg+ (3L/4) F = 0 (3L/4) F=(L/4)(M/2)g 3 F=(M/2)g F=(M/6)g

  24. Define Angular Momentum L Think of rotational inertia I kind of like mass for now. rotating like this with  Magnitude of Angular Momentum L = I

  25. Define Angular Momentum L Think of rotational inertia I kind of like mass for now. Direction of L is given by the RHR rotating like this with  Magnitude of Angular Momentum L = I Rotation This way

  26. What do you mean by rotational analog to mass? Rotational Inertia Depends not only on the amount of mass in the object but also on how the mass is distributed about the axis of rotation : I can change!Formula not really important, but the idea is that the further mass is from the axis of rotation, the greater I Example: Same mass, same volume but arranged differently r2 r1 rotates this way rotates this way I1 I2 >

  27. What do you mean by rotational analog to mass? Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I Disk of mass m Thin ring of mass m Point mass m r r r

  28. What do you mean by rotational analog to mass? Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I Disk of mass m Thin ring of mass m Point mass m r r r I = mr2

  29. What do you mean by rotational analog to mass? Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I Disk of mass m Thin ring of mass m Point mass m r r r I = mr2 I = mr2

  30. What do you mean by rotational analog to mass? Rotational Inertia the idea is that the further mass is from the axis of rotation, the greater I Disk of mass m Thin ring of mass m Point mass m r r r I = mr2 I = mr2 I = (1/2)mr2

  31. Question

  32. Question

  33. Why does a figure skater start spinning faster when she pulls her arms in? Initial initial Final final <

  34. Assume ice surface is frictionless, the net torque on the skater is zero… Net Angular Impulseext = ∆ L = ave.ext x ∆ t = 0 Angular Momentum Lskater is conserved! Initial L initial,skater = I initial,skater initial Final L final,skater = I final,skater final I initial,skater initial = I final,skater final Remember I initial,skater >I final,skater So when the rotational inertia decreases (which it does when she pulls her arms in), angular velocity must increase in order to conserve the angular momentum Spin control is nothing but invoking Conservation of Angular momentum!

  35. Newtonian Model Ouch… Umm why does an apple fall ?? I tried to understand the force on an apple and its relation to apple’s motion. It is all summarized in Newton’s Laws of Motion. Sir. Isaac Newton

  36. Newton’s first law: If the momentum changes, there is a net force on the system. If the momentum is not changing, there is no net force on the system. Newtonian ModelNewton’s Laws of Motion Net Impulseext = ∆ p = ∑ Fave.ext x ∆ t Newton’s second law: Quantitatively relates instantaneous change in momentum (or velocity) to net force ( ∑ Fave.ext= ∆ p /∆ t ) in terms of instantaneous time rate change of momentum… ∑ Fext= d p /dt = m dv/dt = ma An unbalanced force (∑ Fext 0) causes a change in motion of an object,i.e.time rate change of velocity (acceleration)

  37. Newton’s first law: If the momentum changes, there is a net force on the system. If the momentum is not changing, there is no net force on the system. Newtonian ModelNewton’s Laws of Motion Net Impulseext = ∆ p = ∑ Fave.ext x ∆ t Newton’s second law: Quantitatively relates instantaneous change in momentum (or velocity) to net force ∑ Fext= d p /dt = m dv/dt = ma An unbalanced force (∑ Fext 0) causes a change in motion of an object,i.e.time rate change of velocity (acceleration) F A on B = – F B on A Newton’s third law: You cannot push without being pushed yourself!

  38. Air France Concorde Mach 2.23 = 7.58 x 102 m/s << Speed of light (3 x 108 m/s) When is Newtonian Model valid ? When things are not too small and its motion not too fast Protons + Neutrons Electrons

  39. We know aconcorde,What is F ejected gason the concorde? We know the gravitational forces between all the planets and the sun. When/Where is next total solar eclipse? How is Newtonian Model useful ? We know the net force on the object and want to know what its subsequent motion is OR We know the motion of an object and want to know details of the forces acting on the object

  40. Practice Newton’s Laws of Motion

  41. Practice Newton’s Laws of Motion

  42. Practice Newton’s Laws of Motion

  43. Practice Newton’s Laws of Motion

  44. Position vs Velocity vs Acceleration

  45. Position vs Velocity vs Acceleration

  46. Be sure to write your name, ID number & DL section!!!!!

More Related