6. A vehicle of mass 1200 kg is moving with a constant speed of \(40 \mathrm {~ms} ^ { - 1 }\) around a horizontal circular path which is on a test track banked at an angle of \(60 ^ { \circ }\) to the horizontal. There is no tendency to sideslip at this speed. The vehicle is modelled as a particle.

1. Calculate the normal reaction of the track on the vehicle.
2. Determine
   1. the radius of the circular path,
   2. the angular speed of the vehicle and clearly state its units.
3. What further assumption have you made in your solution to (b)? Briefly explain what effect this assumption has on the radius of the circular path.