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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

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Physics 1A, Section 2

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  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

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