How Do You Calculate the New Angular Speed of Coupled Wheels?

[1MileCrash]

Homework Statement

I really don't understand what to do next.

A wheel is rotating freely with an angular speed of 950rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with twice as much rotational inertia of the first is suddenly coupled on the shaft.

What is the new angular speed?

Homework Equations

The Attempt at a Solution

No external torques, so conservation of momentum must be observed.

I is the rotational inertia of the wheel spinning at 950rev/min;

2I is the rotational inertia of the wheel that is coupled.

wf is the final angular speed.


Iw = (I + 2I)wf

wf = Iw/(3I)

wf = w/2I

Right? I can substitute w in, but nothing to substitute in for I. How do I solve this problem?

 

[collinsmark]

Homework Statement

I really don't understand what to do next.

A wheel is rotating freely with an angular speed of 950rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with twice as much rotational inertia of the first is suddenly coupled on the shaft.

What is the new angular speed?

Homework Equations

The Attempt at a Solution

No external torques, so conservation of momentum must be observed.

Very nice. I like your way of thinking.

(By the way, I'm assuming here that when the problem statement says "rotational inertia," it's the same thing as "moment of inertia." I don't hear the term rotational inertia used very often. Even though moment of inertia is the more standard terminology, I'm guessing that your textbook/coursework uses rotational inertia to mean the same thing. Whatever the case, I, like you, am assuming that the I of the second wheel is twice that of the first, and the second wheel is initially at rest.)

I is the rotational inertia of the wheel spinning at 950rev/min;

2I is the rotational inertia of the wheel that is coupled.

wf is the final angular speed.


Iw = (I + 2I)wf

Once again, very nice.

wf = Iw/(3I)

Everything is on track and just fine.

wf = w/2I

Gwahhh!

Try that last simplification again.

 

[1MileCrash]

Thanks, I got it this morning. Stupid, stupid error.