1 / 18

Review from Last Lecture

Review from Last Lecture. Elastic & Inelastic Collisions Momentum conserved Energy conserved in elastic but not in inelastic Rocket Propulsion No “pushing against,” but conservation of momentum Rotational Kinematics Analogous to linear kinematics. Rotational Kinetic Energy.

Download Presentation

Review from Last Lecture

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. Review from Last Lecture • Elastic & Inelastic Collisions • Momentum conserved • Energy conserved in elastic but not in inelastic • Rocket Propulsion • No “pushing against,” but conservation of momentum • Rotational Kinematics • Analogous to linear kinematics

  2. Rotational Kinetic Energy • What is the kinetic energy of a spinning object? • Just the sum of it’s parts!

  3. Moment of Inertia • What is the moment of inertia of an extended object • Break it up into little pieces

  4. Integrals • Recall: All the differential calculus you need (in 5 minutes)

  5. Integrals • Now, all the integral calculus you need in 10

  6. Integrals • A definite integral is just a sum • The “area under the curve” • Consider • Sum of rectangles • Width: dx • Height: kx • Area of triangle • Half base times height • A = ½ a ka • From integration formula ka kx x a

  7. Moments of Inertia • Moment of inertia of a hoop or a thin cylinder • All the mass is at the same R!

  8. Moments of Inertia • Moment of inertia of a disk or solid cylinder • Consider ring at r, with volume 2prLdr

  9. Moments of Inertia • Moment of inertia of a thin rod about CM

  10. Moments of Inertia

  11. Moments of Inertia • What about an arbitrary axis? • Use “Parallel Axis Theorem” I = ICM + MD2 • Moment of inertia about any axis is just moment of inertia about center of mass plus moment of inertia of “CM” about the axis

  12. Moments of Inertia • What about an arbitrary axis? • “Parallel Axis Theorem”

  13. Torque • If angular acceleration (a) is analogous to acceleration (a), what is analogous to force (F)? • Since a = rac, use t = rFc =rF sinf • Call it “Torque” (like a it too is a vector)

  14. Torque and Angular Acceleration • Consider a particle at position r • What are the kimematics? • Analogous to F=ma (linear) we have t=Ia (angular)

  15. Torque and Angular Acceleration • What about for extended object? • Net torque gives rise to angular acceleration

  16. Work and Power • Work and power for a rotating object

  17. Example: Trapdoor • What is acceleration of tip when horizontal? • What is speed of tip when vertical?

  18. Rolling Motion • For a rolling object the point in contact with the surface in momentarily stationary • Thus, center (also CM) moves thru a distance s=rq, at a velocity v=rw • Top moves at speed 2vCM • Kinetic energy is rotation plus translation

More Related