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Physics 1A, Section 2. November 11, 2010. Translation / Rotation. Quiz Problem 25. Quiz Problem 25. Answer: a) T = a(mR 2 + I )/[R(R-r)] f = a( I + mrR)/[R(R-r)] b) m min = a(kR + r)/[g(R-r)] c) rolls to the right. Moment of Inertia. Moments: 0 th moment: ∫dm = mass

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## Physics 1A, Section 2

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**Physics 1A,Section 2**November 11, 2010**Quiz Problem 25**• Answer: • a) T = a(mR2 + I)/[R(R-r)] • f = a(I + mrR)/[R(R-r)] • b) mmin = a(kR + r)/[g(R-r)] • c) rolls to the right**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**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**Monday, November 15:**• Quiz Problem 32 (collision with rotation) • Optional, but helpful, to try these in advance.

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