# Wheels linked by belts: find the one with the least rate of rotation

1. May 11, 2015

### Confused101

1. The problem statement, all variables and given/known data
See Diagram

2. Relevant equations
See Diagram

3. The attempt at a solution
I have been looking for hours for the correct formula but do not know what to use or where to start. If you can point me in the direction of the right formula if one is needed, and I would be very grateful. Is it something to do with velocity ratios ? Thanks

2. May 11, 2015

### SammyS

Staff Emeritus
Physics is much less about finding formulas than it is about analyzing a situation & finding relationships.

Start at one end of the chain of pulleys or the other. Star at A or start at G.

If pulley A makes one complete rotation, how many rotations will pulley B make?

etc.

3. May 11, 2015

### DaveC426913

You don't need a formula. You just need logic and patience.

A belt going from a smaller wheel to a larger wheel reduces the rotation rate.
A belt going from a larger wheel to a smaller wheel increases the rotation rate.

So G is actually going the <strike>slowest</strike> [ edited ] fastest of all.

[ Derp - Sammy beat me to it. ]

Last edited: May 11, 2015
4. May 11, 2015

### Staff: Mentor

So you start with A and notice that as A turns 1 revolution it will turn B say 1/2 rev.
Since B turns 1/2 then C turns 2 revs...

Then review the speeds of revolutions to get the answer.

5. May 11, 2015

### Staff: Mentor

I think you meant to say B, right?

6. May 11, 2015

### Staff: Mentor

Sorry, I just wanted to show the first step or two. I was actually composing my post before I saw yours.

7. May 11, 2015

### SammyS

Staff Emeritus
OK.

I deleted my previous reply to you.

8. May 11, 2015

### Confused101

The correct answer is B as you can see on the diagram. I get to start at A - Lets say it turns once, which caused B to turn half. If B is attached to the Blue B behind then that turns a quarter yes. which turns C red pulley half, and C Yellow pulley will turn once and if you go on like that G then turns only a 1/4 and I think should be the answer compared to B which only turns 1/2

9. May 11, 2015

### SammyS

Staff Emeritus
Both pulleys at B rotate together. Both rotate 1/2 turn, or both rotate 1/4 turn.

10. May 11, 2015

### Confused101

Nope Just do not see it I am afraid. If A turns once and B turns 1/2 then surely C should turn once again - how do you make it 2 ?

11. May 11, 2015

### DaveC426913

Perils of too much editing.
I actually meant G is fastest of all. I didn't want to give him the answer directly, just show him the logic and let him work it out.
I've fixed. it.

12. May 11, 2015

### DaveC426913

Consider starting somewhere other than A. Both A and C are going to turn faster than B (since they're smaller) so you know they're not the answer.

13. May 11, 2015

### Confused101

Guys. I have been staring at this for 4 hours so maybe you would like to talk me through the first 4 - 5 steps starting from A please

14. May 11, 2015

### DaveC426913

Don't start at A. Start anywhere else.

Start at C.
B rotates slower than C.
D rotates the same as C.
E rotates faster than D.
etc.

15. May 11, 2015

### Confused101

I work logically so starting at A seems a good a place as any. If A turns once, then B turns half. If B turns half, then C should turn once or is it twice ? and can you explain to me which is correct and how you worked it out, then I can go from there thanks .

16. May 11, 2015

### DaveC426913

How's that working out for you?

It not as good as anywhere else because it's the most complex and most confusing.

17. May 11, 2015

### Confused101

Again how do you get from 1/2 B to 2 at C . I can only see it as 1 at C. It is half the size of the Blue wheel in B which has turned Half so thus its rotation is double that which is 1. The yellow C pulley which attached to the outer red should also then only turn once no ?

18. May 11, 2015

### scientific601

From B to C is a factor of x2. So the current speed of 0.5 will increase to 1.

19. May 11, 2015

### Confused101

Thanks for your help Scientific601. So A turns once, and B turns 0.5. C turns x 2 of B which is 1 turn. C turns once, so D turns once. If D turns once, then E turns x 4, so turns 4 times. If E turns 4 times, then F turns x 8. If F turns 8 then G turns 4 times. So B is the answer as it turns only 1/2 rotation. Is this correct. ?

20. May 11, 2015

### scientific601

Barring any computational errors, yes. As the screenshot's answer agrees. The slowest in the train.