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A bicycle is classified by the diameter of its tires. For example, a 20-inch bicycle has tires that are 20 inches in diameter.

The number of times a bicycle tire rotates in a given period of time is directly related to the distance traveled in that period of time.

 

  1. A 26-inch bicycle is pedaled so that the tires rotate at a rate of 200 revolutions per minute. A 20-inch bicycle is pedaled so that its tires rotate at a rate of 200 revolutions per minute, as well. What is the linear velocity of each bicycle? State your answers in inches per minute, rounded to the nearest tenth. 
    1. Answers  16,328 and 12,560
  2. Typically, the speed at which a bicycle moves is expressed in miles per hour. Convert the linear velocity of the 26-inch bicycle and the 20-inch bicycle to miles per hour. Round your answer to the nearest tenth.
  3. How many more revolutions must the 20-inch bicycle complete to have the same linear velocity as the 26-inch bicycle? Round your answer to the nearest tenth.
  4. What is the angular velocity of each bicycle? Write your answer in exact form in radians per second.
  5. How many complete rotations does either bike complete in one second? Answer in a complete sentence.
 Apr 3, 2020
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A bicycle is classified by the diameter of its tires. For example, a 20-inch bicycle has tires that are 20 inches in diameter.

The number of times a bicycle tire rotates in a given period of time is directly related to the distance traveled in that period of time.

 

Hello Guest!

 

 
1. Ein 26-Zoll-Fahrrad wird in die Pedale getreten, sodass sich die Reifen mit einer Geschwindigkeit von 200 Umdrehungen pro Minute drehen. Ein 20-Zoll-Fahrrad wird so in die Pedale getreten, dass sich seine Reifen ebenfalls mit einer Geschwindigkeit von 200 Umdrehungen pro Minute drehen. Was ist die Lineargeschwindigkeit jedes Fahrrads? Geben Sie Ihre Antworten in Zoll pro Minute an, gerundet auf das nächste Zehntel. 1.Antworten 16.328 und 12.560

2. Typischerweise wird die Geschwindigkeit, mit der sich ein Fahrrad bewegt, in Meilen pro Stunde ausgedrückt. Konvertieren Sie die Lineargeschwindigkeit des 26-Zoll-Fahrrads und des 20-Zoll-Fahrrads in Meilen pro Stunde. Runden Sie Ihre Antwort auf das nächste Zehntel.

 

1.

\(v=d\pi n\\ v_{26}=26in\cdot \pi\cdot 200/min\)

\(v_{26}=16336\ in/min\)

\(v_{20}=20in\cdot \pi\cdot 200/min\)

\(v_{20}=12566\ in/min\)

 

2.

\(v_{26}=16336\cdot \frac{in}{min}\cdot \frac{miles}{63360in}\cdot \frac{60min}{h}\)

\(v_{26}=15.5\ miles/h\)

 

\(v_{20}:v_{26}=20:26\\ v_{20}=\frac{15.5\cdot 20}{26}\ miles/h\\ \)

\(v_{20}=11.9\ miles/h\)

laugh  !

 Apr 3, 2020
edited by asinus  Apr 3, 2020

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