Chapter 12
 2. (a) zero            (b) zero
    (c) 80 km/h +x dir  (d) 1500 m/s² 
    (e) 80 km/h -x dir  (f) 1500 m/s²
    (g) 80 km/h +x dir  (h) zero
    (i) 160 km/h +x dir (j) 1500 m/s² 
    (k) zero            (l) 1500 m/s²
 6. solid cylinder - you must explain why
 8. (a) 4 N left        (b) 0.6 kg m²
10. (a) mg(R-r)         (b) (Krot/Ktot) = 2/7
    (c) (17/7)mg
14. (a) (0.11 m)omega   (b) 2.06 m/s² left
    (c) 46.8 rad/s² CW  (d) 1.18 s
    (e) 8.60 m          (f) 6.07 m/s
16. (a) 0.884 s         (b) 9.39 J
    (c) 1.41 m/s        (d) 0.120 J
    (e) 442 rad/s       (f) 9.27 J
26. (a) (600 kg m²/s)k
    (b) (720 kg m²/s)k
46. (a) 0.933 rad/s     (b) 98 J
    (c) 8.4 rad/s       (d) 882 J
    (e) calculate work done by each skater
        during pull; adding together yields
        784 J, the amount of increase in K
50. 1310 m/s
54. 2.57 rad/s
56. 0.06995 rad/s
34. (a) 0.528 kg m²/s
    (b) 440 rad/s

Chapter 14
16. (a) 16.5 N  (b) 2.46 times the radius of the Earth
32. (a) 22.2 MJ (b) 69.5 MJ
34. 24.2 km/s
36. (a) 38.3 MJ (b) 1030 km
54. (2pi)sqrt(r³/G(M+(m/4)))
58. (a) 1/2     (b) 1/2    (c) B by 114 MJ
Online Problem G1. 0.070 N less
Serway Problems - Chapter 12
41. (a) v2 = sqrt(2Gm1²/(m1+m2)d);
        v1 = sqrt(2Gm2²/(m1+m2)d);
        v_relative = sqrt(2G(m_1+m_2)/d)
    (b) K_1 = 1.07 x 10^32 J; K_2 = 2.67 x 10^31 J
49. proof - HINT: After writing the 2nd Law for each
    star, write the velocity of each star in terms
    of the radius of that star's orbit and the time
    to go around once, then add the two equations.
Fishbane Problems - Chapter 8
 6. (a) proof
    (b) r1/r2=m2/m1
Fishbane Problems - Chapter 12
35. 2.99 km/s
55. (a) 1660 m
    (b) 2.83 m/s
    (c) yes; 1.76 m/s
Chapter 16
 6. (a) 1230 N/m    (b) 76 N
16. 21.6 cm
18. (a) 24.8 cm     (b) 2.23 Hz
20. (a) 0.500 m
    (b) -0.251 m
    (c) 3.06 m/s
30. (a) 1.11 Hz     (b) 0.050 m
32. (a) 200 N/m     (b) 1.39 kg   (c) 1.91 Hz
34. (a) 7.25 MN/m   (b) 49,416
36. (a) mv/(m+M)
    (b) mv/sqrt((m+M)k)
38. (a) -(80 N)cos((2000 rad/s)t-(pi/3))
    (b) 3.14 ms
    (c) 4 m/s
    (d) 0.08 J
40. (a) 0.735 kg m² 
    (b) 0.024 N m/rad
    (c) 0.181 rad/s
48. (a) 0.869 s     (b) 6.25 cm
58. (a) (r/R)sqrt(k/M)
    (b) sqrt(k/M)
    (c) zero
64. 4.97 cm