Circular Motion: Finding Angular Velocity in a System of Interconnected Wheels

[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?

 

[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

 

[donjt81]

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

but since the speed of smaller wheel is 407 rad/s won't the larger wheel speed be the same?

so is the answer to the problem 407 rad/s for the larger wheel? but that doesn't make sense because the larger wheel is supposed to go slower...

I am confused...

 

[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:

w_small x r_small = w_large x r_large

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

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

 

[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)?

 

[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

 

[donjt81]

ok thanks

my final answer was 37.9866 rad/s

does that sound about right?

 

[BerryBoy]

Exactly what I got

 

[donjt81]

thanks for all your help

 

[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.