A penny is put on a rotating turntable. when on the platter does the penny need the most centripetal force...?

Question

to stay in it's place.


why?

Answer 1

If the turntable is frictionless it will slide off anywhere at any speed.

Fc=mV^2/R or since angular velocity w = V/R
Fc= m w^2 R
the onlly force that counteracts Fc is force of friction f

f=umg

so when f<=Fc the penny will fly off

umg <= m w^2 R

ug <= w^2 R
w >= sqrt (ug/R)

Curious to note that mass has nothing to do with when only coefficient of friction u and distance from the center R.