A wheel has a radius of 3.92 m. How far (path length) does a point on the circumference travel if the wheel is rotated through an angle of 38.7°?

Question

A wheel has a radius of 3.92 m. How far (path length) does a point on the circumference travel if the wheel is rotated through an angle of 38.7°?

How far does a point on the circumference travel if the wheel is rotated through an angle of 38.7 rad?

How far does a point on the circumference travel if the wheel is rotated through an angle of 38.7 rev?

Answer 1

Hey Hope,

The basic process for each of these will be to figure out how many revolutions each question involves, then multiply that by the circumference of the circle (remember C = 2 * pi * R

1. The third question is the easiest. Just multiply 38.7 times the circumference.
2. For the other 2, we can set up a conversion factor:
3. 38.7 deg x (1 revolution/ 360 degrees) = total number of revolutions
4. ^^^ you are multiplying by "1" here, since there are 360 degrees in one revolution
5. For radians, it's a similar process, but 1 revolution = 2*pi radians.