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76. We choose positive coordinate directions (different choices for each item) so that each is accelerating positively, which will allow us to set a1 = a2 = Rα (for simplicity, we denote this as a). Thus, we choose upward positive for m1, downward positive for m2 and (somewhat unconventionally) clockwise for positive sense of disk rotation. Applying Newton’s second law to m1, m2 and (in the form of Eq. 11- 37) to M , respectively, we arrive at the following three equations. T1 −m1g = m1a1 m2g − T2 = m2a2 T2R− T1R = Iα (a) The rotational inertia of the disk is I = 12MR 2 (Table 11-2(c)), so we divide the third equation (above) by R, add them all, and use the earlier equality among accelerations – to obtain: m2g −m1g = ( m1 +m2 + 1 2 M ) a which yields a = 425 g = 1.6 m/s 2. (b) Plugging back in to the first equation, we find T1 = 2924m1g = 4.6 N (where it is important in this step to have the mass in SI units: m1 = 0.40 kg). (c) Similarly, with m2 = 0.60 kg, we find T2 = 56m2g = 4.9 N. Main Menu Chapter 1 Measurement Chapter 2 Motion Along a Straight Line Chapter 3 Vectors Chapter 4 Motion in Two and Three Dimensions Chapter 5 Force and Motion I Chapter 6 Force and Motion II Chapter 7 Kinetic Energy and Work Chapter 8 Potential Energy and Conservation of Energy Chapter 9 Systems of Particles Chapter 10 Collisions Chapter 11 Rotation 11.1 - 11.10 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 - 11.20 11.11 11.12 11.13 11.14 11.15 11.16 11.17 11.18 11.19 11.20 11.21 - 11.30 11.21 11.22 11.23 11.24 11.25 11.26 11.27 11.28 11.29 11.30 11.31 - 11.40 11.31 11.32 11.33 11.34 11.35 11.36 11.37 11.38 11.39 11.40 11.41 - 11.50 11.41 11.42 11.43 11.44 11.45 11.46 11.47 11.48 11.49 11.50 11.51 - 11.60 11.51 11.52 11.53 11.54 11.55 11.56 11.57 11.58 11.59 11.60 11.61 - 11.70 11.61 11.62 11.63 11.64 11.65 11.66 11.67 11.68 11.69 11.70 11.71 - 11.80 11.71 11.72 11.73 11.74 11.75 11.76 11.77 11.78 11.79 11.80 11.81 - 11.90 11.81 11.82 11.83 11.84 11.85 11.86 11.87 11.88 11.89 11.90 11.91 - 11.100 11.91 11.92 11.93 11.94 11.95 11.96 11.97 11.98 11.99 11.100 11.101 - 11.103 11.101 11.102 11.103 Chapter 12 Rolling, Torque, and Angular Momentum Chapter 13 Equilibrium and Elasticity Chapter 14 Gravitation Chapter 15 Fluids Chapter 16 Oscillations Chapter 17 Waves—I Chapter 18 Waves—II Chapter 19 Temperature, Heat, and the First Law of Thermodynamics Chapter 20 The Kinetic Theory of Gases Chapter 21 Entropy and the Second Law of Thermodynamics Chapter 22 Electric Charge Chapter 23 Electric Fields Chapter 24 Gauss’ Law Chapter 25 Electric Potential Chapter 26 CapacitanceChapter 27 Current and Resistance Chapter 27 Current and Resistance Chapter 28 Circuits Chapter 29 Magnetic Fields Chapter 30 Magnetic Fields Due to Currents Chapter 31 Induction and Inductance Chapter 32 Magnetism of Matter: Maxwell’s Equation Chapter 33 Electromagnetic Oscillations and Alternating Current Chapter 34 Electromagnetic Waves Chapter 35 Images Chapter 36 Interference Chapter 37 Diffraction Chapter 38 Special Theory of Relativity Chapter 39 Photons and Matter Waves Chapter 40 More About Matter Waves Chapter 41 All About Atoms Chapter 42 Conduction of Electricity in Solids Chapter 43 Nuclear Physics Chapter 44 Energy from the Nucleus Chapter 45 Quarks, Leptons, and the Big Bang
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