Answer:
a) 2.15 m
b) 123 m
c) 772.8 m
Explanation:
Circular Motion
One point located at a distance r from the center of rotation travels a distance L given by the arc length :
[tex]L= \theta r[/tex]
Where [tex]\theta[/tex] is the angle formed during the rotation.
The wheel described in the question has a radius r=4.1 m and a point on the wheel rotates some angles given in each part:
a) [tex]\theta=30^o=30\cdot \pi / 180=\pi/6 \ rad[/tex]
Calculating L
[tex]L= \pi/6 \cdot 4.1=2.15 \ m[/tex]
b) [tex]\theta=30\ rad[/tex]
[tex]L= 30 \cdot 4.1=123 \ m[/tex]
c) [tex]\theta = 30\ revolutions = 30\cdot 2\pi\ rad=60\pi \ rad[/tex]
[tex]L= 60\pi \cdot 4.1=772.8 \ m[/tex]
