# Circular motion question

1. Nov 10, 2005

### donjt81

This is the question...

A small wheel of radius 1.4cm drives a large wheel of radius 15cm by having their circumferences pressed together. If the small wheel turns at 407 rad/s, how fast does the larger one turn? Answer in rad/s

This is what I was thinking...

radius of smaller wheel = .014m
radius of larger wheel = .15m

circumference of smaller wheel = 2*pi*r = 2*3.14*.014 = .08792
angular velocity of smaller wheel (given) = 407 rad/s

angular velocity = circumference/time
time = circumference/angular velocity
=.08792/407 = .000216s

circumference of larger wheel = 2*pi*r = 2*3.14*.15 = .942

angular velocity = circumference/time

Does this approach look right?

2. Nov 10, 2005

### BerryBoy

I disagree... By intuition, you can predict that the larger wheel is going to turn more slowly.. Try another approach..

Hint: Consider the fact that the speeds of circumferences are equal.

Eq: speed = w x r

w = angular velocity

Does this help?

Sam

Last edited: Nov 10, 2005
3. Nov 10, 2005

### donjt81

You are right... the larger wheel should go slower.

but since the speed of smaller wheel is 407 rad/s wont the larger wheel speed be the same?

so is the answer to the problem 407 rad/s for the larger wheel? but that doesnt make sense because the larger wheel is supposed to go slower...

I am confused...

4. Nov 10, 2005

### BerryBoy

OK, so if the speed at the circumfrence is:

v = w x r (as I stated above).

If the wheels are in contact this speed is equal on both wheels (not the angular velocity). Therefore:

wsmall x rsmall = wlarge x rlarge

I can't give you anymore hints without doing it now.

Good Luck... Let me know what you get for an answer.
Sam

Last edited: Nov 10, 2005
5. Nov 10, 2005

### donjt81

ohh i got it. i was confused between angular velocity (w) and tangential velocity(v).

Hey another question. do you know if i did the right thing by converting the radius to (m) or should i have left it as (cm)?

6. Nov 10, 2005

### BerryBoy

You could have left it as cm because you're dividing by the other length (which should have the same units).

I usually convert thing to metres at the start though, its good practice in my experience.

Sam

7. Nov 10, 2005

### donjt81

ok thanks

8. Nov 10, 2005

### BerryBoy

Exactly what I got

9. Nov 10, 2005