Calculate the frequency of rotation when a coin flies off a turntable

[M1N]

Homework Statement

Hi. I have tried and tried and I just can't figure this one out. I'm assuming the outer coin flies off first, then the inner coin. I'm assuming for that to happen, the rotation frequency must be higher (or do both coins come off at the same time or the inner coin before, with the inner coin not needing to have as high a velocity?) I believe the relationship between the velocities is v_outer = 4v_inner. I am not sure how to get the frequency for the inner coin (I have working out for different ideas but it's quite a mess so I won't include it here, but my thought process is expressed above) Any help will be greatly appreciated. Thanks!

Relevant Equations

v = wr, w = 2pif, F = mv^2/r, v = 2pir/T, T = 1/f,

 

[erobz]

You need to share your attempt to receive help via forum rules.

 

[haruspex]

I'm assuming the outer coin flies off first, then the inner coin.

ok, but why?

I'm assuming for that to happen, the rotation frequency must be higher (or do both coins come off at the same time or the inner coin before, with the inner coin not needing to have as high a velocity?) I believe the relationship between the velocities is v_outer = 4v_inner.
Relevant Equations: v = wr, w = 2pif, F = mv^2/r, v = 2pir/T, T = 1/f,

Which of those equations have you tried to use?

 

[kuruman]

ok, but why?

The last sentence in the posted screenshot of the statement of the problem says "When the frequency of the rotation reaches 3.00 Hz the outer coin (2) flies off the disk." Physical reasoning aside, it is fair to assume that the coin mentioned is the one that slides first because it provides the data for predicting when the second coin will slide.

 

[haruspex]

The last sentence in the posted screenshot of the statement of the problem says "When the frequency of the rotation reaches 3.00 Hz the outer coin (2) flies off the disk." Physical reasoning aside, it is fair to assume that the coin mentioned is the one that slides first because it provides the data for predicting when the second coin will slide.

Providing the rotation rate at which the inner coin flies off would also work, so the text is not definitive.
But I was hoping to elicit some physical reasoning.

 

[M1N]

You need to share your attempt to receive help via forum rules.

Hi. I have added my working out now. Sorry!

 

[M1N]

The last sentence in the posted screenshot of the statement of the problem says "When the frequency of the rotation reaches 3.00 Hz the outer coin (2) flies off the disk." Physical reasoning aside, it is fair to assume that the coin mentioned is the one that slides first because it provides the data for predicting when the second coin will slide.

Hi. The problem is, in my working it appears I am going back to the same 'moment' in time when the outer coin flies off. I don't know how to show when it is flying off. My working suggests the inner coin should fly off at the same frequency of rotation and thus at the same time, but I am not sure if this is right. Question c says to find the relationship between the velocities of the inner and outer coin when they are flying off. When I put the velocity of the inner coin flying off (1.32m/s) and the radius into the equation v = wr it just gives the same period of 6pi, and when I put that into w = 2pi/T or 2pif I get the same frequency of 3.00Hz. What am I missing?

 

[erobz]

What am I missing?

For starters, I don’t see Newtons Second law anywhere in that handwritten mess( sorry for being frank). Please see latex guide. That is how we wish to interact mathematically.

 

[kuruman]

What am I missing?

You are manipulating equations that relate linear and rotational displacements and velocities hoping that the answer will somehow pop out. It will not because, as @erobz noted, you have not considered Newton's second law that governs the motion of the coins. There is a force that accelerates them and causes them to go around in a circle but only up to the point when they slide off.

So you need to consider in terms of forces (a) what must be true for a coin to go around in a circle and (b) what must be true for a coin to slide off.