Next, calculate the linear speed of the 26-inch bicycle being pedaled at a rate of 200 revolutions per minute. Express your answer in inches per minute rounded

Question

i think im going to have a mental breakdown

Answer 1

The circumference of the wheel is 2*pi*radius = 2*3.14*26 = 37.7 inches.  This is how far the bike moves forward in one revolution of the wheel.  The problem states that the bike is moving at 200 revolutions per minute (rpm).  That equates to a linear speed of:

 

(200 rpm)*(37.7 inches per revolution) = 7539.8 inches per minute

 

Mental breakdown averted!

Answer 2

The 26 inches = 0.66 meter is the wheel's diameter; therefore, the radius is 0.33 meter.

The rotating speed is 200 rev/min = (200 * 2 * pi/60) rad/sec = (20 * pi/3) rad/sec.

The linear speed = rotating speed * radius

                         = (20 * pi/3) * 0.33 

                         = 6.91 meters/sec

                         = 272.0472 inches/(1/60 min)

 

                         = 16,322.8  inches/minute

Answer 3

Dr Phillips method is great, but he forgot that that a bike is measured by the bike tires Diameter and not the radius.  Phongi remembered about bike measurements and used radians/second which is a very skilled thing to do.  If you are in geometry and not trigonometry, or pre-calculus you may not have learned that yet.  

 

If you are in Geometry then:

C=πd       Formula Given for Circumference

C=π(26 in)   Substitute in value for bike tire diameter

C≈3.14(26 in)  Substitute approximate value for π

C≈81.64 in     Simplify, 

 

So you know it travels 81.64 inches every time it goes one full revolution.  Let's continue.

 

Given:  The bike tire goes around 200 times every minute, that is the 200 rev/min.

 

200 rev/min (81.64 in/rev) ≈ 16,328 in/min.  (notice that the rev's cancel out)