Question

HELP PLEASE angular velocity EASY!!! Will award MEDALand FAN! Picture attached below.

Answer 1

First find the circumference of the tire. Which is pi*diameter. So we have this:
26pi inches for the circumference of the tire.

As the ant travels around the tire, the ant will travel 26pi inches in one revolution of the tire.

Since we want the answer in revolutions per minute, we will need to convert hours into minutes and miles into inches.

We look up the conversion for miles to inches and find that there are 63,360 inches in one mile. We also know that there are 60 minutes in one hour.

So our setup looks like this.

\[\frac{ 1Revolution }{ 26\pi inches }* \frac{ 63,360 inches }{ 1 mile }* \frac{ 10 miles }{ 1 hour }* \frac{ 1 hour }{ 60 minutes }\]The inches, miles and hour cancel each other out. So we have this:\[\frac{ 1 revolution * 63,360 * 10 *1 }{ 26\pi *1 *1*60 minutes }\] Which equals this:\[\frac{ 633,600 revolutions }{ 1,560\pi minutes }= 129.3 \frac{ revolutions }{ minute}\]