Question

1. A wheel has a radius of 4.1 m. How far (path length) does a point on the wheel travel if the wheel is rotated through angles of 30◦ , 30 rad, and 30 revolutions, respectively?

Answer 1

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 :

$L= \theta r$

Where $\theta$ 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) $\theta=30^o=30\cdot \pi / 180=\pi/6 \ rad$

Calculating L

$L= \pi/6 \cdot 4.1=2.15 \ m$

b) $\theta=30\ rad$

$L= 30 \cdot 4.1=123 \ m$

c) $\theta = 30\ revolutions = 30\cdot 2\pi\ rad=60\pi \ rad$

$L= 60\pi \cdot 4.1=772.8 \ m$