Which Coin Flies Off First from a Speeding Turntable?

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SUMMARY

The discussion centers on determining which of two coins on a speeding turntable flies off first, with Coin 1 positioned closer to the center than Coin 2. Despite initial calculations suggesting Coin 1 would be ejected first due to its lower radius, the consensus, supported by the answer manual, indicates that Coin 2 actually flies off first. This conclusion is based on the understanding of centrifugal acceleration and the relationship between radius and angular velocity, specifically that Coin 2 experiences greater centrifugal force due to its larger radius.

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  • Centrifugal acceleration principles
  • Understanding of angular velocity and its calculations
  • Basic physics of friction and its role in circular motion
  • Knowledge of the relationship between radius and force in rotational dynamics
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  • Explore the concept of centrifugal force in detail
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alingy1
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Two coins are on a turntable that steadily speeds up, starting from rest, with a ccw rotation. Which coin flies off the turntable first?

Coin 2 is further away than coin 1.


MY ATTEMPT:

I believe centrifugal acceleration is done by friction. So fs=us*m*g. Fc=mv^2/r.
Then, v=sqroot(us*g*r).
Suppose coin 2 is at radius 2(r1), (r1) being the distance from center of coin 1.
angular velocity 1= r1(sqroot(us*g))
angular velocity 2=2r1(sqroot(us*g))

So, I conclude that coin 1 must be thrown off first. HOWEVER, the answer manual says it is coin 2, which is an obvious answer for me too. But, I can't seem to be able to prove it.
 
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Your expressions for angular velocity are not right.
Check again.
The velocity (v) is OK.
 
Ok, I rearranged it. I now understand! v=wr indeed!
Is there any easier way to think about this problem?
 

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