Mechanics Teacher
Wheels Radius / Distance Traveled
Note to the teacher
On these pages, students will learn about the relationships between wheel radius, diameter, circumference, revolutions
and distance. Students will use formulas relating these measurements to compute the distance a wheel of given radius
travels for a given number of wheel revolutions. Students will have to use both fractions and decimals to make these calculations. While the worksheet is designed to help students learn the geometry of the circle and the relationship between
wheel size, revolutions and distance, and may be completed by students with little background in these areas, the existing
ability to multiply fractions and decimals will be necessary to successfully complete the worksheet. Teachers may wish to
review any or all of these skills depending on their students’ background.
Note that there are no instructions regarding rounding. The answers assume rounding to 2 digits beyond the decimal
place, except for known fractions. Teachers may wish to supply additional instructions. If they do not, students’ answers
will vary slightly according to what rounding conventions they use.
The illustration below explains and reinforces the relationships between radius, diameter and circumference.
Radius is the measurement of a straight
line from the center of a circle to the edge.
Radius will always equal one half diameter.
©2005 Robomatter Inc. RE 2.5_RW 1.1
Diameter is the measurement of a
straight line across the center of an object
(in this case a wheel).
5.14
The circumference of a circle is the total
distance around its outside. Circumference
equals the diameter of the circle times
π (pi), which is about 3.14. One revolution
of a wheel will make it move a distance
equal to its circumference.
Teacher Mechanics
Wheels Radius / Distance Traveled
Instructions
Based on the information provided about the wheels shown on these pages, calculate how far they will travel.
An example is shown below. Complete the information on the following pages.
Example
If the wheel below makes one revolution, how far will it go? Use the tables below to find the answer.
2.
Diameter
Radius
1
1.5625”
x
2
π (pi)
Diameter
2
3.125”
x
Circumference
19 /16"
1.
3
9.81”
=
3.14
Circumference
=
1
9.81”
Distance
Revolutions
x
3.125”
=
9.81”
After reviewing the concepts, students are expected to use the following procedure:
•
•
•
•
•
•
•
Identify the radius written below a pictured wheel (1.)
Enter it in the box labeled “Radius”
Multiply the radius by 2 to calculate the diameter and enter this number in the box labeled “Diameter”
Multiply this diameter by π, simplified to 3.14, to find the circumference
Find the number of revolutions specified in the instructions (2.)
Enter it in the box labeled “Revolutions”
Multiply this number by the number calculated for circumference to find the distance the wheel will travel
Approximate classroom time: 10-20 minutes depending on students’ background
5.15
©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Wheels Radius / Distance Traveled
Students successfully completing the worksheet will be able to:
1.
2.
3.
4.
5.
6.
7.
Identify radius from a labeled drawing
Describe the geometry of a circle
Describe the relationship between radius, diameter, circumference, revolutions and distance for a wheel
Calculate diameter from radius
Calculate circumference from diameter
Calculate distance from wheel circumference and revolutions
Multiply decimals and fractions
Standards addressed:
Math Standards
Numbers and Operations
Algebra
Geometry
Measurement
Problem Solving
Technology Standards
The Nature of Technology Standards 1; Design 8, 9
Note: Workbook answers begin on the next page.
©2005 Robomatter Inc. RE 2.5_RW 1.1
5.16
Teacher Mechanics
Wheels Radius / Distance Traveled
Radius is the measurement of a straight
line from the center of a circle to the edge.
Radius will always equal one half diameter.
Diameter is the measurement of a
straight line across the center of an object
(in this case a wheel).
The circumference of a circle is the total
distance around its outside. Circumference
equals the diameter of the circle times
π (pi), which is about 3.14. One revolution
of a wheel will make it move a distance
equal to its circumference.
Instructions
Based on the information provided about the wheels shown on these pages, calculate how far they will travel.
An example is shown below. Complete the information on the following pages.
Example
If the wheel below makes one revolution, how far will it go? Use the tables below to find the answer.
Diameter
Radius
1
1.5625"
x
3.125"
x
Circumference
19 /16"
3
5.17
3.14
1
3.125"
Circumference
=
9.81"
Distance
Revolutions
x
9.81"
=
π (pi)
Diameter
2
2
=
9.81"
©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Wheels Radius / Distance Traveled
Instructions
Based on the information provided about the wheels shown on these pages, calculate how far they will travel.
If the wheel below completes 1.75 revolutions, how far will it go? Use the tables below to find the answer.
Diameter
Radius
1
.47”
x
15/32"
.94”
x
Circumference
3
2.95”
=
π (pi)
Diameter
2
2
3.14
Circumference
=
1.75
2.95”
Distance
Revolutions
x
.94”
=
5.16”
If the wheel below completes 2 3 /16 revolutions, how far will it go? Use the tables below to find the answer.
Diameter
Radius
1
.625”
x
1.25”
=
π (pi)
Diameter
2
2
x
3.14
1.25”
Circumference
=
3.93”
5/8"
Circumference
3
©2005 Robomatter Inc. RE 2.5_RW 1.1
3.93”
5.18
Distance
Revolutions
x
2.19
=
8.61”
Teacher Mechanics
Wheels Radius / Distance Traveled
Instructions
Based on the information provided about the wheels shown on these pages, calculate how far they will travel.
If the wheel below completes 1.75 revolutions, how far will it go?
Normally it’s much easier to calculate decimal numbers, rather than fractions, so the
first thing we’ll do is convert the fraction to a decimal. 15 /32" converts to .47".
We know that the circumference–the distance a wheel will travel in one
revolution—is equal to π x D where D is the diameter. Since the Radius, R, is equal
to half of the diameter, we can change the equation from C = π x D to:
C = π x (2R), or, 2 x π x R.
If we substitute the values in the equation, we can see that:
C = 2 x 3.14 x .47" = 2.95".
15/32"
Since the wheel makes 1.75 revolutions, the total distance traveled is:
distance = 2.95 inches / revolution x 1.75 revolutions = 5.16 inches.
If the wheel below completes 2 3/16 revolutions, how far will it go?
As we saw earlier, calculations are much easier when using decimals, rather than
fractions. So the first thing we’ll do is convert both numbers, the radius and the number
of revolutions, to decimals.
The radius of 5/8" converts to 0.625” and the number of revolutions converts from
2 3/16 to 2.19.
To find the circumference, we’ll use the equation from the previous problem,
C = 2 x π x R or C = 2 x 3.14 x .625" = 3.93".
5/8"
Since the wheel makes 2.19 revolutions, the total distance traveled is:
distance = 3.93 inches / revolution x 2.19 revolutions = 8.61 inches.
Again, because of round off, your students’ answers may be slightly different.
5.19
©2005 Robomatter Inc. RE 2.5_RW 1.1