Conceptual understanding of circular motion

[cmwilli]

[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.

 

[tiny-tim]

hi cmwilli!

… 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!)

 

[cmwilli]

What does LHS mean?

 

[tiny-tim]

Left-hand side!

(of the equation)

 

[rwisz]

Circular motion is a type of motion where an object moves along a circular path. In this type of motion, the object's velocity is constantly changing, but its speed remains constant. This change in velocity is due to the presence of a force, known as the centripetal force, which acts towards the center of the circular path.

In the case of the image provided, the person is moving along a circular path on a spinning platform. The force that is keeping the person on the platform and causing the circular motion is not the weight of the person, but rather the normal force exerted by the platform on the person. This normal force is perpendicular to the surface of the platform and acts as the centripetal force in this scenario.

The reason why the weight of the person is not equal to the centripetal force is because the weight is a force due to gravity, which acts downwards towards the center of the Earth. This force is not directly involved in causing the circular motion, but rather the normal force from the platform is responsible for that.

In order for an object to undergo circular motion, there must be a net force acting towards the center of the circular path. This is known as the centripetal force, and it is related to the object's speed, radius of the circular path, and mass. The equations you have provided, such as a=v^2/r and f=ma, are used to calculate the centripetal force in different scenarios.

In summary, the conceptual understanding of circular motion involves understanding that it is a type of motion where an object moves along a circular path, and the centripetal force is the force that keeps the object moving in that path. The weight of an object is not always equal to the centripetal force, as it depends on the specific scenario and the forces involved.