Solutions

1. In order convert from degrees to radians, we must remember that 360^o = 2p radians. Therefore, multiplying the number of degrees by 2p/360 converts the values. For the listed values, this gives:
   30^o = 30^o (6.28/360^o) = .523
   45^o = 45^o (6.28/360^o) = .785
   60^o = 60^o (6.28/360^o) = 1.05
   90^o = 90^o (6.28/360^o) = 1.57
   180^o = 180^o (6.28/360^o) = 3.14
   270^o = 270^o (6.28/360^o) = 4.71
   360^o = 360^o (6.28/360^o) = 6.28
2. If we assume that the acceleration of the potter's wheel is constant, then we know that the w_f = w_i + at. Using the given data, we get:
   
   0.20 rev/s = 0 rev/s + a(30 s)
   a = (0.20 rev/s)/(30 s) = .0067 rev/s²
   
   We need to convert this answer to rad/s². To do this, we multiply the answer by 2p/1 rev, giving
   
   a = (2p rad/rev)(.0067 rev/s²) = .042 rad/s²
   
3. The first thing that we must assume is that the wheels of the car are not slipping with respect to the road. If this is the case, then we know that the angular velocity and acceleration are given by
   
   w = v/r = (17.0 m/s)/(.480 m) = 35.4 rad/s
   a = a/r = (2.00 m/s²)/(.480 m) = 4.17 rad/s²
   
   Using this data, we can calculate the angular difference by
   
   DQ = (35.4 rad/s)(5.00 s) + .5(4.17 rad/s²)(5.00 s)²
   DQ = 177 rad + 52.1 rad = 229 rad
   
   To convert this answer to revolutions, we multiply the answer by 1 rev/2p rad. This gives (229 rad)(1 rev/6.28 rad) = 36.5 revolutions.