# Pulley and rotation problem

## Homework Statement

A tractor has a belt pulley diameter of 10 inch operating at 1100 revolutions per minute. The pulley is connected by a belt to another machine that needs to operate at 650 rpm. What size should the pulley be on the second machine?

2Pi*r

## The Attempt at a Solution

I don't really know where to start. I know that a wheels circumference is 2Pi*r
The first wheel is 10 inches so
2*Pi*5 inches = 1100rpm
if the second wheel has to operate at 650
can I get it by 650/2pi=103 inches?

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Integral
Staff Emeritus
Gold Member
Set up a simple ratio.

$$\frac {1100} {10} = \frac {650} x$$

thank you

I'm still a bit unclear. Sorry.
If I set up a ratio
1100/10=650/x
I get an answer of 5.9
I need the second wheel to rotate slower but if it is smaller wont it spin faster?

I tried this again.
This seems to work.

driven pulley rpm= drive pulley rpm * drive pulley diameter/driven pulley diameter

650rpm=1100rpm*10inch/x
650x=11000
x=16.923 inch diameter for the pulley