(Rotational Motion) Calculating maximum velocity.

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To calculate the maximum velocity of an object on a spinning disk without slipping, it's essential to derive the correct equation based on the forces involved. Two equations, V=sqrt(μ*r*g) and V=sqrt((μ*g)/R), were presented, but one is dimensionally incorrect and should be identified. A free body diagram should be drawn to analyze the forces at play when the object is on the verge of slipping. Understanding the context and conditions under which these equations were derived is crucial for their application. Proper definitions of the variables are necessary to ensure the equations are used correctly.
KANY3EUWEST
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Homework Statement


If I have an object with mass M. Place it on a spinning disk at radius R and the coefficient of friction is μ what is the maximum velocity I can spin the disk without the object slipping? I have the actual values for the problem, but I'm much more interested in how to get there.

Homework Equations


I've found two equations online that pertain to this scenario, but they're completely different. V=sqrt(μ*r*g) and V=sqrt((μ*g)/R)

The Attempt at a Solution


I haven't made an attempt as I'm not exactly sure which equation to use, or if either are correct.
 
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Where did you find these equations? Under what conditions were they derived?
I suggest that you derive your own equation. Start by drawing a free body diagram of the object at the moment when it is just about ready to slip. So make an attempt and post it.

On edit: One of the two equations you posted is not even appropriate to be a velocity. Which one is it?
 
KANY3EUWEST said:
V=sqrt(μ*r*g) and V=sqrt((μ*g)/R)
Equations are meaningless out of context. They need to be accompanied by definitions of the variables and a description of the circumstances in which they are valid.
Are such provided at those links? Do they match the circumstance you have?
As kuruman points out, if in those equations the variables stand for what one would guess, one of them is dimensionally wrong. Which one?
 
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