Answer :
1) In a circular motion, the angular displacement [tex]\theta[/tex] is given by
[tex]\theta = \frac{S}{r} [/tex]
where S is the arc length and r is the radius. The problem says that the truck drove for 2600 m, so this corresponds to the total arc length covered by the tire: [tex]S=2600 m[/tex]. Using the information about the radius, [tex]r=0.35 m[/tex], we find the total angular displacement:
[tex]\theta = \frac{2600 m}{0.35 m} =7428 rad[/tex]
2) If we put larger tires, with radius [tex]r=0.60 m[/tex], the angular displacement will be smaller. We can see this by using the same formula. In fact, this time we have:
[tex]\theta = \frac{2600 m}{0.60 m}=4333 rad [/tex]
[tex]\theta = \frac{S}{r} [/tex]
where S is the arc length and r is the radius. The problem says that the truck drove for 2600 m, so this corresponds to the total arc length covered by the tire: [tex]S=2600 m[/tex]. Using the information about the radius, [tex]r=0.35 m[/tex], we find the total angular displacement:
[tex]\theta = \frac{2600 m}{0.35 m} =7428 rad[/tex]
2) If we put larger tires, with radius [tex]r=0.60 m[/tex], the angular displacement will be smaller. We can see this by using the same formula. In fact, this time we have:
[tex]\theta = \frac{2600 m}{0.60 m}=4333 rad [/tex]