How to figure out an angle in radians?

Question

The rear wheels of a tractor have a diameter of 1.5 meters, and the front wheels have a diameter of 0.7 meters. The tractor travels a distance of 35 meters. What angle in radians must the wheels turn?

 

I think the part that's throwing me off is the question itself.. wouldn't a wheel always turn 360 degrees? Thanks for your help!

Answer 1

Yes the wheel turns 360^o in one turn, but it's turning several times.  If the wheel turns twice for example, it turns through 360^o*2 = 720^o (4pi radians).  The equation, in radians, is:

 

     θ*radius = distance

 

For the rear wheels:

 

      radius = (1.5 m)/2 = 0.75 m     

      θ*0.75 = 35

 

For the front wheels:

 

     radius = (0.7 m)/2 = 0.35 m

     θ*0.35 = 35

 

Solve for θ in each case  (θ will be in radians).