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# Math Help

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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.

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?

Apr 16, 2021
edited by Guest  Apr 16, 2021

#1
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Number 1. I got 7539.8 don't really have time to explain also can anybody go to my post it is the one abount two line p and q intersect at X at an angle of 38 degrees. thx

Apr 16, 2021
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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.

Linear  velocity f 26 inch  bike =  13  * 2pi * 200  =  16336.3 in /min

Linear  velcity of 20 inch  bike  =  10 * 2pi *200  =   12566.5 in / min

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.

26 in bike  =   16336.3 in  x    1 ft  / 12 in  x   1 mile  / 5280 ft   x 60  =  15.5 mph

20 in bike  =    12566.5 in  x   1 ft / 5280 x     1mile  / 5280 ft x   60   =   11.9 mph

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.

10 * 2pi  *  R   =   16336.3

R  =  16336.3  / ( 20pi)    =  260

So....the  20 in bike  must rotate  60  more  revs per minute  to have  the  same linear velocity as  the 26 in bike

4.What is the angular velocity of each bicycle? Write your answer in exact form in radians per second.

Since  each  rotates  200 times in a minute....they  have  the  same  angular velocity

This  is     200 * 2pi  /60   =  (20/3) pi  rads   /sec

5.How many complete rotations does either bike complete in one second?

(20/3) pi   =  6 + 2/3 rotatations per sec  =   6 full rotations per sec   Apr 16, 2021
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Thank you so much CPhil god bless you

Guest Apr 16, 2021