Calculating Centrifugal Force for a Bug on a Spinning Compact Disc

[Robertoalva]

1. A bug crawls outward from the center of a compact disc spinning at 230 revolutions per minute. The coefficient of static friction between the bug's sticky feet and the disc surface is 1.2. How far does the bug get from the center before slipping?

Homework Equations

fs ≤ μs n

The Attempt at a Solution

I'm trying to get the centrifugal force of the disc. Then substitute the ms by 1.2 and multiply for the force, but I don't remember the formula to get the centrifugal force.

 

[voko]

The trajectory of the bug (ignoring its slow outward crawl) is a circle. What is acceleration in uniform circular motion?

 

[Robertoalva]

F= m (v^2)/r

and the velocity is 2pi r w right?

 

[haruspex]

F= m (v^2)/r

and the velocity is 2pi r w right?

Usually ω is expressed in radians/sec, which means you don't need the 2pi. But as long as you do the right conversions the above equations are fine.

 

[voko]

Right, if w is in revolutions per unit of time.

 

[Robertoalva]

r≤ (μs g)/ 4π^2 ω^2 that's where I got stuck right now. g is obviously 9.81 and you said that ω= the 230 revolutions per minute, right?

 

[voko]

You must use one system of units in the computations. 9.81 uses seconds, 230 uses minutes, which is not compatible. Convert either one.

 

[Robertoalva]

so then I divide 230/60 to get it in seconds? now it all makes sense

 

[voko]

Good.

 

[Robertoalva]

Thank you very much!