Circular motion question (1 Viewer)

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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?
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?

Last edited:
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...
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.
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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)?
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?

ok thanks

my final answer was 37.9866 rad/s

does that sound about right?
:smile: Exactly what I got
thanks for all your help

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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