Understanding the Relationship Between Mass and Inertia in Circular Motion

AI Thread Summary
The discussion centers on the relationship between mass, inertia, and the banking angle of curves in circular motion. It highlights that while mass affects inertia, the required banking angle for a curve is independent of mass, leading to confusion about how these concepts interact. The participants analyze Newton's first law and centripetal force equations, noting that mass cancels out in the equations governing circular motion. This cancellation suggests that the banking angle does not depend on mass, which aligns with the original question. Ultimately, the conversation clarifies that the independence of the banking angle from mass is a key point in understanding circular motion dynamics.
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Homework Statement



The Mass of an object doesn't affect the angle at which a curve must be banked. The law of inertia, however, states that the motion of any object is affected by its inertia, w/c depends on its mass. How can objects rounding banked curves obey the law of inertia if the amount of banking required for a curve of a given radius of curvature and speed is independent of mass?

Homework Equations





The Attempt at a Solution


Totally clueless! >.<

I just know it has something to do with N1:

Newton's first law of motion states that "An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force."

...and Fc=mv2/R
 
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Ok, so mv^2/r is the centripetal acceleration that needs to be balanced by a frictional force. How does the equation for that frictional force depend on m?
 
hmmm ok...so

Fc = mv2/R

Ff = mu*Fn
= mu*mg

Fc = Ff
mv2/R = mu*mg

so the masses cancel out?

...the thing is I don't even get what the question is asking?
 
Yes, the mass cancels out. Isn't that what the question is asking? There should be an angle in your friction but that's not even terribly important. The acceleration is proportional to mass and so is the friction.
 
but am i not just proving what was already stated in the question? Which is that radius and speed don't rely on mass?

I'm just terribly confused of the question...shouldn't I incorporate N1 in my conclusion but I just don't seem to get it...
 
I think you should read the question again. It looks to me like it's asking why is the banking angle independent of mass if the inertia is dependent on mass. If the mass cancels, isn't that the answer? Am I reading it wrong? How are you reading it?
 
Oooo that makes more sense...thanks for rephrasing it!

maybe I was just complicating the question...

Thanks again for your help. ^^,
 

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