Mass on a rotating turntable problem.

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The discussion revolves around analyzing the forces acting on a mass placed on a rotating turntable. It highlights that the normal force equals the weight of the block in the vertical direction, while static friction acts to the left in the horizontal direction. A centripetal force is necessary for circular motion, which is provided by friction, leading to the equation Fc = Ff. The relationship between the speed of the turntable and the block is established as omega*R, where omega is the angular velocity and R is the radius. The conversation concludes with a suggestion to calculate the time required for the block to reach the necessary speed.
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[PLAIN]http://img841.imageshack.us/img841/7913/314pw.jpg

I'm having a bit of trouble with this one.

So the FBD of the block.

In the y coordinates, the normal equals its weight

in the x coordinates, we have static friction to the left, and is there a force to the right? There as to be right, since it eventually begins translating radially?

Just looking for a little guidance, thanks!
 
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From the point of view of the outside observer, a centripetal force is required to hold the mass in circular motion. This is provided by the force of friction. So you begin with Fc = Ff, put in the details and calculate the speed for which they are just equal.
 
the speed of the turntable and the block or just equal?

omega*R?
 
Yes, the speed of the turntable omega*R.
Then you can go for the time to reach that speed.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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