1 / 15

Second Midterm Exam

This is the second midterm exam for Mechanics, covering topics introduced after the first exam. Topics include kinetic energy, work, conservative forces, potential energy, conservation of energy, momentum, conservation of momentum, rotational kinematics, torque, angular momentum, integration, moments of inertia, parallel axis theorem, and rolling motion.

laurencea
Download Presentation

Second Midterm Exam

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. Second Midterm Exam • One week from today: • Wednesday, October 25th • Same rules as 1st exam • Covers only topics introduced after 1st exam • Chapters 7-11 in Serway & Jewitt • Kinetic Energy, Work, Conservative Forces, Potential Energy, Conservation of Energy • Momentum, Conservation of Momentum • Rotational Kinematics, Torque • Angular Momentum • A practice exam is available on the website

  2. Review from Last Lecture • Integration • Moments of Inertia • Parallel Axis Theorem • Rolling Motion

  3. Example: Giant Yo-Yo • When one pulls on rope, does spool move right or left?

  4. Example: Giant Yo-Yo • When one pulls on rope, does spool move right or left? • Depends on torque about pivot point (contact with floor)

  5. Example: Giant Yo-Yo • When one pulls on rope, does spool move right or left? • Depends on torque about pivot point (contact with floor) • If rope projects to a point behind pivot, rolls right

  6. Example: Giant Yo-Yo • When one pulls on rope, does spool move right or left? • Depends on torque about pivot point (contact with floor) • If rope projects to a point behind pivot, rolls right • If rope projects in front, rolls left

  7. Example: Massive Pulleys • With massive pulleys, now have to take moment of inertia of disk into account • Equation for each part • Solve I r T2 m2 T1 m1

  8. Torque as a Vector • Torque is a vector • Magnitude • What is direction? • Define torque vector with cross product of position and force vectors

  9. The Vector Cross Product • If C = A x B, then • C = AB sinq • Direction of C given by Right Hand Rule • Properties

  10. The Vector Cross Product • Unit Vectors and the algebraic form of cross product

  11. Angular Momentum • Consider the torque on a particle • Call L = r x p the angular momentum (of the particle about the origin)

  12. Example: Airplane Overhead • What is the angular momentum of a plane flying overhead? • It’s not zero! • Even if plane is flying level • Note that L has a constant magnitude with a direction into the page v q h r

  13. Angular Momentum • Now consider a system of particles • Like force and momentum, the net torque gives the rate of change of angular momentum

  14. Spinning Rigid Objects • What’s the angular momentum of a spinning, rigid object? • Always measure from (and perpendicular to) axis of rotation (which is along z axis)

  15. Spinning Rigid Objects • What happens when we apply a torque to a spinning object?

More Related