Conceptual understanding of circular motion

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Centripetal force is not equal to a person's weight because it is determined by the net force acting towards the center of the circular path. The equation F = ma for radial motion shows that the centripetal force is the difference between gravitational force (mg) and the normal force (N). In non-rotational scenarios, this difference is zero, but during circular motion, the normal force is less than the gravitational force. The confusion arises from the common definition of weight as mg, while the actual weight felt is the normal force. Understanding this distinction clarifies the dynamics of circular motion.
cmwilli
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[PLAIN]http://img207.imageshack.us/img207/37/capturebg.jpg



a=v^2/r
v=2pir/T
f=ma



So I already have the answers to all the questions. The problem I am having is I don't understand why the centripetal force is not equal to the weight of the person. If it isn't the weight what force, other than gravity, is acting on him that would be called the centripetal force.
 
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hi cmwilli! :smile:
cmwilli said:
… I don't understand why the centripetal force is not equal to the weight of the person. If it isn't the weight what force, other than gravity, is acting on him that would be called the centripetal force.

i think the book is correct, but rather confusing

the F = ma equation for the radial (vertical) direction, for someone standing on the ground, is mg - N = mv2/r

the total centripetal force is the LHS, mg - N (so, for no rotation, it would be zero), but the weight (ie, what would show up if he was standing on a weighing machine) is the reaction force N, which is less than mg

the book is confusing because we usually call mg the weight, although technically our weight is what we feel, ie the reaction force, N, against us (which is usually the same as mg, but not in this case!) :smile:
 
What does LHS mean?
 
Left-hand side! :biggrin:

(of the equation)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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