1 / 10

Physics 1A, Section 2

Physics 1A, Section 2. November 15, 2010. Translation / Rotation. Moment of Inertia. Moments: 0 th moment: ∫dm = mass useful 1 st moment: ∫ r dm (1/M) ∫ r dm is the center of mass useful 2 nd moment: ∫R 2 dm = moment of inertia R is the distance from the axis of rotation

ghita
Download Presentation

Physics 1A, Section 2

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 1A,Section 2 November 15, 2010

  2. Translation / Rotation

  3. Moment of Inertia • Moments: • 0th moment: ∫dm = mass • useful 1st moment: ∫ r dm (1/M) ∫ r dm is the center of mass • useful 2nd moment: ∫R2 dm = moment of inertia • R is the distance from the axis of rotation • Other ways to write the integral: ∫dm = ∫ dV = ∫∫∫ dx dy dz • Moment of inertia examples: • Frautschi et al. Table 14.1, page 379 • Parallel axis theorem: I = ICM + Md2

  4. Quiz Problem 41

  5. Quiz Problem 41 • Answer: • a) I1 = 8prda4 • I2 = ½ prda4 • I1/I2 = 16 • b) wf = 16w/17 • c) No, some lost to friction. • Kfinal/Kinitial = 16/17

  6. Quiz Problem 24

  7. Angular Momentum • Angular momentum vector L is constant, in the absence of outside torques. If there are outside torques, dL/dt =  • Single particle: L = r x p = m r x v r = distance (vector) from a fixed reference point • System of particles: L = Mtotrcm x vcm +  mjr´j x v´j orbital spin (about c.m.) r´j, v´j measured with respect to center of mass • Rotating rigid body: Lspin = I (for principal axis) I =∫R2 dm = moment of inertia R = distance from rotation axis

  8. Quiz Problem 24

  9. Quiz Problem 24 • Answer: • a) L = 2MRv • b) I = 3MR2 • c) w = (2/3) v/R • d) 1/3 is lost

  10. Thursday, November 18: • fluid mechanics

More Related