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Definition/Summary
Centripetal force is not a separate force.
It is only an alternative name for the radially inward component of tension or friction or other force or forces on a body.
In a free body diagram, centripetal force should never be mentioned by name (it should be called "tension" "friction" etc), and should not be shown at all if it there is no actual force in the centripetal direction.
Equations
Extended explanation
The friction force can be centripetal:
A vehicle driving uniformly along a circular path on flat ground experiences a friction force towards the centre of the circle: that is the only force on the vehicle with a component in that direction.
In that case, the friction force may be called the centripetal force.
A vehicle driving uniformly along a circular path on banked ground experiences a friction force down the bank.
A vehicle changing speed along any circular path experiences a friction force with both a tangential and a radial component.
In either case, there is no separate radial force, though some people like to call the radial component of friction the centripetal force.
Tension can be centripetal:
A block on a flat surface attached by string or elastic to a fixed point experiences a tension force along the string.
In that case, the tension force may be called the centripetal force.
A mass attached by string to a fixed point and rotating in a horizontal circle below it also experiences a tension force along the string, but this is obviously not centripetal.
Drawing a centripetal force on the diagram for this situation is very unhelpful, since there is no actual force there, though some people like to call the horizontal component of the tension the centripetal force.
Free body diagrams:
In a free body diagram, centripetal force should never be mentioned by name (it should be called "tension" "friction" etc), and should not be shown at all if it is only the component of a force or forces.
In a free body diagram in an inertial frame, centripetal acceleration may be shown by a different sort of arrow (doubled or squiggly), completely separate from the body it relates to.
Centrifugal force in a rotating frame:
By comparison, in a free body diagram in a rotating (non-inertial) frame, the centrifugal force is a separate force and should be shown.
* This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!
Centripetal force is not a separate force.
It is only an alternative name for the radially inward component of tension or friction or other force or forces on a body.
In a free body diagram, centripetal force should never be mentioned by name (it should be called "tension" "friction" etc), and should not be shown at all if it there is no actual force in the centripetal direction.
Equations
Extended explanation
The friction force can be centripetal:
A vehicle driving uniformly along a circular path on flat ground experiences a friction force towards the centre of the circle: that is the only force on the vehicle with a component in that direction.
In that case, the friction force may be called the centripetal force.
A vehicle driving uniformly along a circular path on banked ground experiences a friction force down the bank.
A vehicle changing speed along any circular path experiences a friction force with both a tangential and a radial component.
In either case, there is no separate radial force, though some people like to call the radial component of friction the centripetal force.
Tension can be centripetal:
A block on a flat surface attached by string or elastic to a fixed point experiences a tension force along the string.
In that case, the tension force may be called the centripetal force.
A mass attached by string to a fixed point and rotating in a horizontal circle below it also experiences a tension force along the string, but this is obviously not centripetal.
Drawing a centripetal force on the diagram for this situation is very unhelpful, since there is no actual force there, though some people like to call the horizontal component of the tension the centripetal force.
Free body diagrams:
In a free body diagram, centripetal force should never be mentioned by name (it should be called "tension" "friction" etc), and should not be shown at all if it is only the component of a force or forces.
In a free body diagram in an inertial frame, centripetal acceleration may be shown by a different sort of arrow (doubled or squiggly), completely separate from the body it relates to.
Centrifugal force in a rotating frame:
By comparison, in a free body diagram in a rotating (non-inertial) frame, the centrifugal force is a separate force and should be shown.
* This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!