Ferris Wheel

by Hannah Ryan

| 9 QuestionsThe toy ferris wheel has a radius of 13 inches pictured below:

The point C is the center of the wheel and a point P on the circle is chosen. After the ferris wheel has moved forward a distance of d, the point P moves to a new point on the circle, marked N.

A. Complete the table below, showing how the angle NCP varies with the distance d that the wheel has traveled forward:

Angle Measurements in Degrees:

1

1 pt

1 inch =

2

1 pt

10 inches =

3

1 pt

3 feet =

4

1 pt

7 feet =

B. Remember that one radian is the measure of the angle cut out by a one unit length arc on a circle with radius one unit so m(a) = 1 radian in the picture below:

More generally, a counterclockwise angle of r radians is the angle cut out by an arc of length r units on a unit circle. Using this definition of radian angle measure, complete the table below, showing how the angle NCP varies with the distance d that the wheel has traveled forward:

Angle Measurements in Radians:

5

1 pt

1 inch =

6

1 pt

10 inches =

7

1 pt

3 feet =

8

1 pt

7 feet =

9

1 pt

C. What is the relationship between the measure of an angle in degrees and its measure in radians?

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