The wheel of a car is 60cm in diameter. Find the angle of rotation of the wheel when the car moves forward by a horizontal distance of 100cm

Question

It shows a enlarged view of a wheel and the diameter of the wheel is 60 cm. It asks find the angle of rotation when the car moves 100cm horizontally

Answer 1

Hello John,

 

There are two ways (and possibly more :-) ) in which you can go about this.  If the formula s = r * θ looks familiar from your notes, then look at option 1.  Otherwise, please scroll down to option 2.

 

(Option 1)

For s = r * θ,

s is the arc length,

r is the radius of the circle (half the diameter)

θ is the angle of rotation (for this formula, θ is in radians)

 

Dividing both sides of s = r * θ by r yields

θ = s/r (I did this since we will be looking for θ).

 

From the story problem:

s = 100cm, since that is how much arc length from the circle will travel the ground as it rotates.

r = 30cm, since the radius of a circle is half the diameter.

 

So θ = 100/30 = 10/3 radians (again, I emphasize this formula yields an answer in radians).

 

If looking for an answer in degrees, you will need to multiply by the conversion ratio of 180°/π,

to get (600/π)° ≈ 191°.

 

(Option 2)

You can set up a proportion, using

(θ / 360°) = (s / (2Π*r))

s is the arc length,
r is the radius of the circle (half the diameter)
θ is the angle of rotation (for this formula, θ is in degrees)

 

From the story problem:
s = 100cm, since that is how much arc length from the circle will travel the ground as it rotates.
r = 30cm, since the radius of a circle is half the diameter.

 

θ / 360° = 100 / (2Π * 30).  Multiplying both side by 360°, yields

θ ≈ 191°.

 

And if you need your answer in radians,

use the reciprocal of the conversion ratio mentioned above: π/180°, yielding

θ = 10/3

 

Hope the above help, and thank you for the question.

 

Kind regards,

Michael E.