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
=.942/.000216 = 4361.11 rad/s

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
r = radius

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.

What was your final answer?

Sam

7. Nov 10, 2005

donjt81

ok thanks

my final answer was 37.9866 rad/s

does that sound about right?

8. Nov 10, 2005

BerryBoy

Exactly what I got

9. Nov 10, 2005

donjt81

thanks for all your help

10. Nov 10, 2005

BerryBoy

Anytime,

Glad to help. I joined this forum to get help, but giving help is just as useful to me, boosts my understanding too.

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