P5

    q = 200 rad   # of rev = 200 rad/2p = 31.8 rev      

P19   

 f (rev/s) = 100 rev / 0.02 s = 5,000 rev/s = 5,000 x 2p rad/s = 31,415 rad/s      

P27   

      a = -5 rad/s/s        f = 200 rpm

      w = 2pf = 400p  rad /m = 21 rad/s

      t = w/a = 21/5 s = 4.2 s

P41

      V3 = 2 m/s,     w3 = V3 / R3 = 2 (m/s)/ 0.24 m

  V5 = w3 x 0.12 = 2 0.12/0.24 = 1 m/s

       V5 /0.2 = V4 /0.15 so that V4 /0.15 = V5 (0.15/0.2) = 0.75 m/s

P51

              wf = wi + at             qf = qi + wi t + (1/2)at**2

      t = 2p x 20/(60x5) = 0.41 s       qf = (1/2) x 5 x 0.41 x 0.41 /2p = 0.067 turn

     L = 2p R x 0.067 = 3.14 x 0.067 = 0.2 m

P71   

     480 N x 3 = Fb x 12,    so that   Fb = 120 N

          480 N x 9 = Fd x 12,    so that   Fd = 360 N

          Fb x 4 = Fa x 12,          so that   Fa = Fb / 3 = 40 N

          Fc = 80 N

P77

 (1) SF = 0   (Translational Equilibrium)   
 (2) St = 0   (Rotational Equilibrium) 

      From (2):  1000 x 1 = -Fay x 2,       so that   Fay = -500 N (down)

               Fcy x 2 = 1000 N x 3,       so that  Fcy = 1500N

               Fcx x 2 = Fcy x 2,           so that   Fcx = Fcy = 1.5 kN

      From (1):  Fax = -Fcx = -1.5 kN (to the left)    

P107

            I = 1.5 kg.m**2,      w = at ,     a =  w/t = 10/10 = 1 rad/s/s

              t = Ia = 1.5 kg.m.m.rad/s/s = 1.5 (kg.m/s/s).m.rad = 1.5 N.m   

P135

            m = 2x10**-3 kg,       R = 0.5 m,      f= 1 rev/s,

            w = 2pf = 2p,           V = Rw = p  m/s

            L = mRV = 3.14x10**-3   kg.m**2/s