Question

Jane has a bike with a 22-inch rear wheel. The wheel sprocket is 3 inches in diameter and the pedal sprocket is 4 inches in diameter (the sprockets hold the chain.) How fast in miles per hour is she going if she pedals at a rate of 100 revolutions per minute?

Answer 1

Rear-wheel diamater: 22
Wheel sprocket on rear-wheel: 3

Pedal sprocket: 4
AngularSpeed: 100revs/min

R1= radius of rear
W1=angular speed of rear

R2=radius of pedal sprocket
W2=Angular speed of pedal sprocket

(R1)(W1)=(R2)(W2)<-----(EQ1)
Plug in the corresponding values, but before that convert the 100revs into radiance per hour since the problem is asking of "how fast miles/hour"

The angular speed of the Rear-Sprocket and The rear wheel is Equal. The reason is because the sprocket is located on the wheel thus
Angular speed(sprocket)=Angular speed(wheel)

After you get the angular speed of the Rear sprocket on Equation one (EQ1) you can calculate the distance it covers by using the S=R(Theta)

where in the theta must be in radiance* and the radius u must use must be the radius of the wheel since we are looking for the distance of the wheel given a certain angle and radius of course.

Answer 2

pedal sprocket diameter* 4 inches

Answer 3

Be careful of the diameter, u need to divide it by 2 to get the radius.