a We are given that the speedv of an object spinning in a circle equals the circumference of the circle divided by the time T it takes the object to complete one revolution. Let's write the defined speed of a spinning object.
Speed=TimeCircumference
We want to write above formula using the variables v,T, and r (the radius of the circle). To do so, let's first remember the formula for the circumference of the circle.
Circumference=2πr
Now we can substitute Speed=v,Circumference=2πr, and Time=T into the speed formula.
v=T2πr
b We are given that a scooter has tires with a radius of 321 inches and the tires make one revolution every 101 seconds. To find the scooter's speed, we will substitute r=321 and T=101 into the formula that we found in Part A.
We found that the speed of the scooter is about 219.9 inches per second. However, we are asked to find the speed in miles per hour. To do so we will first convert our speed in inches to miles using a conversion factor.
63360inches1mile
Multiplying 219.9 inches by this factor will convert it to miles.
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