Wheels+and+Distance+Study+Guide

How to make a robot go a certain distance.

Robot specifications: Wheel diameter 12.7

How many rotations must a motor be set to using wheels with a 12.7 diameter be programmed to travel in order for it to go 10cm? How many degrees must a robot using wheels with a 40cm circumference be programmed to travel in order for it to go 20cm?

We know that (distance = circumference x rotations) and that 1 rotation equals 360 degrees.

First, find the number of rotations and then use the rotations to determine the degrees.

Get rotations on a side by itself.

distance = circumference x rotations

circumference ||  || = ||   || __circumference__ x rotations circumference ||
 * __...distance....__

circumference ||  || = ||   || rotations ||
 * __...distance....__

40cm ||  || = ||   || rotations || 0.25 = rotations
 * __10cm__

Second, use a proportion to find the degrees. 1 rotation ||  || = ||   || __y degrees__ x rotations || Get y degrees on one side. 1 rotation ||  || = ||   || (__y degrees__) x rotations ||  || (x rotations) ||
 * __360 degrees__
 * (x rotations) || (__360 degrees__)

1 rotation ||  || = ||   || y degrees ||
 * (x rotations) || (__360 degrees__)

(0.25)(360 degrees) = y degrees

90 degrees = y degrees

Finally, tell how many degrees must be put in the program. Program the robot's wheels to turn 90 degrees so the robot will travel a distance of 10cm.

How will switching wheels with a 8cm diameter to wheels with a 2cm diameter affect the distance a robot travels if the program is not changed? Give your answer as a percent.

We know that 2 is 1/4 of 8.

We know that (distance = circumference x rotations) and that (circumference = 3.14 x diameter) so substituting gives

(distance = 3.14 x diameter x rotations).

(1/4)(distance) = (3.14)(1/4diameter)(rotations)

Due to the associative property of multiplication and the fact that the right side only contains multiplication, multiplying the wheel's diameter by 1/4 is the same as multiplying the whole side by 1/4. If one side of this relationship is multiplied by 1/4, the other side must also be multiplied by 1/4 to keep the equal sign true due to the property of equality.

This means that using wheels with 1/4 of the diameter of the original wheels will make the robot go 1/4 the distance or 25% of the original distance.

What is diameter? What is circumference? A theoretical distance is ... An actual distance is ...

Wheel 1: What is the circumference of a wheel that has a diameter of 4.75? Pie x diameter = circumference. 3.14 x 4.74cm = 14.88cm What is the theoretical (predicted) distance traveled in centimeters with three wheel rotations? Circumference x rotations = distance traveled 14.88cm x 3 = 44.65 cm

43.95cm 44.52cm 45.06cm

44.51

3.6cm 3.14 x 3.6cm =

11.3cm

11.3cm x 3 = 33.9cm

33.25cm 33.58cm 34.17cm

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