# Thread: Bike and Sprocket problem

1. ## Bike and Sprocket problem

You are riding a bike along a level road. Assume each wheel is 28 inches in diameter, the rear sprocket has radius 3 inches and the front sprocket has radius r inches. Suppose you are pedaling the front sprocket at the rate of 1.5 rev/sec and your forward speed is 11 mph on the bike. What is the radius of the front sprocket?

So here are the key information:
Wheel is 28 inches in diameter
Rear sprocket has raidus 3 inches
Front sprocket has raidus r inches
Pedaling front sprocket at the rate of 1.5 rev/sec
Forward speed is 11 mph
Find raidus of front sprocket

I'm having trouble putting all this information in my head, can anyone help me through with the steps?

2. ## Re: Bike and Sprocket problem

formula required ...

$\displaystyle v = r \omega$

v is linear speed

$\displaystyle \omega$ is angular speed in radians per unit time

first, a unit conversion ...

11 mph = (968/5) in/sec

since $\displaystyle v = r \omega$ ...

968/5 = 14 $\displaystyle \omega$

$\displaystyle \omega$ = (484/35) radians/sec

angular speed of the rear wheel = angular speed of the rear sprocket

484/35 = (linear speed of the rear sprocket)/3

linear speed of the rear sprocket = (1452/35) in/sec = linear speed of the chain connecting the front and rear sprockets.

now you know the linear speed of the front sprocket. convert the angular speed of the front sprocket from rev/sec to rad/sec and calculate its radius.

3. ## Re: Bike and Sprocket problem

Originally Posted by Chaim
You are riding a bike along a level road. Assume each wheel is 28 inches in diameter, the rear sprocket has radius 3 inches and the front sprocket has radius r inches. Suppose you are pedaling the front sprocket at the rate of 1.5 rev/sec and your forward speed is 11 mph on the bike. What is the radius of the front sprocket?

So here are the key information:
Wheel is 28 inches in diameter
Rear sprocket has raidus 3 inches
Front sprocket has raidus r inches
Pedaling front sprocket at the rate of 1.5 rev/sec
Forward speed is 11 mph
Find raidus of front sprocket

I'm having trouble putting all this information in my head, can anyone help me through with the steps?
How about looking here: Bike and Sprocket Problem

4. ## Re: Bike and Sprocket problem

The intent may have been to find the pedal sprocket size given the 3 in drive sprocket size but as worded the problem is flawed