Say, it's a stone tied to the end of a string. If centripetal force is inwards, how is it balanced? what is tension, where is pointing to in this case? fictitious forces in this case?
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Centripetal force is inwards, yes.
It isn't balanced. The stone is accelerating. (Even though it has constant speed, its velocity is not constant as it changes direction.)
Tension is the centripetal force. Centripetal force is a description of the effect of a force, not the cause. You can always categorize the force by its cause in addition to categorizing it as centripetal. Various common causes of centripetal force:
tension - as in your example
normal force - car on a banked curve
gravity - orbits of planets and moons
magnetic - electron in a cyclotron
Centrifugal force is a fictitious force applying to the stone, that appears to be balanced by tension if you imagine the stone as stationary in its own reference frame. Such a reference frame is non-inertial and Newton's laws don't work.
On the other hand, centrifugal force is also a real force in this example. It acts on the axis holding the string (e.g., your hand). It tends to pull that axis toward the outside of the circle. This is a real force. It's the opposite end of the tension. (Tension is always a force in two directions on two different objects, one on each end of the rope.) It is a balanced force. It is balanced by your strength if you are holding the string. As it it balanced, your arm stays fairly stationary, although you usually cannot react quickly enough to be perfectly stationary.
The example might be clearer in the case of a centrifuge. In this case, the centripetal force is the normal force exerted by the centrifuge on the sample. The centrifugal force is the normal force exerted by the sample on the centrifuge. The centrifuge should be balanced, so there is no force on the axis, but the centrifuge must of course be made of a rigid material to be able to absorb the centrifugal force on its rim. You can imagine, if you made a centrifuge of a rubbery material, it would stretch while in operation, more so when there is a massive sample inside than if there is no sample. This real effect proves that centrifugal force is a real force.
It isn't balanced. The stone is accelerating. (Even though it has constant speed, its velocity is not constant as it changes direction.)
Tension is the centripetal force. Centripetal force is a description of the effect of a force, not the cause. You can always categorize the force by its cause in addition to categorizing it as centripetal. Various common causes of centripetal force:
tension - as in your example
normal force - car on a banked curve
gravity - orbits of planets and moons
magnetic - electron in a cyclotron
Centrifugal force is a fictitious force applying to the stone, that appears to be balanced by tension if you imagine the stone as stationary in its own reference frame. Such a reference frame is non-inertial and Newton's laws don't work.
On the other hand, centrifugal force is also a real force in this example. It acts on the axis holding the string (e.g., your hand). It tends to pull that axis toward the outside of the circle. This is a real force. It's the opposite end of the tension. (Tension is always a force in two directions on two different objects, one on each end of the rope.) It is a balanced force. It is balanced by your strength if you are holding the string. As it it balanced, your arm stays fairly stationary, although you usually cannot react quickly enough to be perfectly stationary.
The example might be clearer in the case of a centrifuge. In this case, the centripetal force is the normal force exerted by the centrifuge on the sample. The centrifugal force is the normal force exerted by the sample on the centrifuge. The centrifuge should be balanced, so there is no force on the axis, but the centrifuge must of course be made of a rigid material to be able to absorb the centrifugal force on its rim. You can imagine, if you made a centrifuge of a rubbery material, it would stretch while in operation, more so when there is a massive sample inside than if there is no sample. This real effect proves that centrifugal force is a real force.
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The centrifugal force that applies to the *stone* is fictitious. The centrifugal force that applies to *your arm* is real.
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