Question 905779: The wheels of a scooter have a diameter of 4.5 inches. If the person riding the scooter is traveling down hill at 15.0 mph. what is the approximate angular speed of the wheels in radians per second?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! angular speed equals the change in angle divided by the change in time.
linear speed equals the change in angle times the radius divided by the change in time.
from these formulas, we can derive:
linear speed equals angular speed times the radius.
angular speed equals linear speed divided by the radius.
the change in the angle is measured in radians.
the change in the angle is equal to the number of revolutions of the circle times 2 * pi.
this is because one full revolution of a circle is equal to 360 degrees which is equivalent to 2*pi radians.
your problem states:
The wheels of a scooter have a diameter of 4.5 inches. If the person riding the scooter is traveling down hill at 15.0 mph. what is the approximate angular speed of the wheels in radians per second.
the scooter is traveling at 15 miles per hour.
we want to translate 15 miles per hour to inches per hour so we multiply 15 * 5280 to get 79200 feet per hour and we multiply 79200 * 12 to get 950400 inches per hour.
now want to translate 950400 inches per hour to inches per second so we divide 950400 inches per hour by 60 to get 15840 inches per minute and we divide 15840 inches per minute by 60 to get 264 inches per second.
we wind up with 15 miles per hour is equivalent to 264 inches per second.
that's the linear speed of the wagon.
since angular speed equals linear speed divided by the radius, we get:
angular speed = 264 / 2.25 = 352/3 radians per second.
in decimal form, this would be equal to 117.33333..... radians per second.
that's your solution as best i can determine.
here's a reference that might help you understand what's happening a little.
http://www.algebralab.org/lessons/lesson.aspx?file=trigonometry_triganglinvelocity.xml
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