Optimizing Grip on a Rotating Vinyl Record: Bug's Position and Weight

[DJ_Froyke]

Homework Statement

A bug is sitting on a rotating vinyl record. Between the bug to the record acts static force. for the bug not to lose it's grip and be thrown outside of the record, he should:
a. sit closer to the center.
b. sit further from the center.
c. lose weight.
d. both a and c are correct.

Homework Equations

Centripetal force: F=mw2R
Friction: F=μmg

The Attempt at a Solution

I think the changing the radius will reduce the centripetal force and will not affect the friction. this it will make the bug's grip more firm and will prevent it from losing grip.
although, losing weight will decrease both the centripetal force and the friction at the same ratio. the ratio between them will stay the same. my teacher said the answer is d.
Who is correct??
Thanks for the help!

 

[PhanthomJay]

It looks like you are, DJ (assuming you chose 'a' and not 'b'!), but your reasoning is not quite correct. When the bug moves closer to the center, the centripetal force decreases, and the friction force also decreases to a value less than uN. That's because the friction force IS the centripetal force. And as long as it is less than or equal to uN, the bug won't slip. In any case, decreasing the mass doesn't matter, because the solution is independent of it.

Welcome to PF!