← Force suppliers, circular-motion analysis, and angular momentum

Centripetal is a role, not a new force

Four lessons, four different forces doing one job. A cord's tension held a whirling yo-yo in its circle. Friction held a turning car. Gravity held the Moon. A wall's normal force held a rotor rider.

So what exactly is the centripetal force: a fifth force, waiting to be added to the list?

No. Count the forces in each of those four cases, and you find no fifth force anywhere.

'Centripetal force' names the role played by real forces such as tension, friction, gravity, or a normal force. It is never an extra force of its own.

It is a job title. Whichever real force points at the circle's center holds the job.

Four scenes, one job titlescenethe real force pointing at the centerthe role it fillsyo-yo on a cordthe cord's tensioncentripetal forcecar on a flat curvefriction from the roadcentripetal forceMoon around EarthEarth's gravitational pullcentripetal forcerotor rider at the wallthe wall's normal forcecentripetal force
Four scenes, four real forces, one job title.

For the whirled yo-yo, the tension is the centripetal force. Not tension plus something extra: just the tension, doing the inward job.

A free-body diagram shows the same thing. For a turning car, the diagram shows three real forces: weight down, the road's normal force up, and friction pointing toward the center. It never shows a separate 'centripetal force' arrow, because no such separate force acts.

weightnormal forcefrictionrear view; the center of the turn is to the left
The turning car's free-body diagram: three real forces. The friction arrow is the centripetal force.

The sorting line sits here: every arrow on a free-body diagram names a real force with an identifiable source. 'Centripetal force' has no source of its own, so it never gets its own arrow.

Does a fourth force act on the car?weightnormal forcefriction'centripetal force'
Does a fourth force act on the car? No. The added arrow is wrong: the friction already is the centripetal force.

For an orbiting satellite, exactly one force acts: the planet's gravitational pull. That one force is the satellite's centripetal force.

When a problem says 'the centripetal force on the bus', read it as the net inward force on the bus, supplied by some real force. Your first move is to name which real force that is, and the object exerting it.

Which statement says what 'centripetal force' means?

One note before the worked examples: in these whirling-cord scenes the cord stays level. The circle is horizontal, and the level cord runs from the object straight toward the center.

A paint can whirls in a horizontal circle on a cord. List the force or forces on the can that point toward the center.

Only the cord acts on the can in the horizontal plane, and the level cord runs toward the center.

So exactly one force points toward the center: the cord's tension.

The tension is the can's centripetal force; no second inward force acts.

One force: the cord's tension. It is the can's centripetal force.

A paint can whirls on a cord. Nestor says: 'The cord's tension is the can's centripetal force. There is no second inward force on the can.' Is he correct?

A free-body diagram of a turning bus shows its weight, the road's normal force, and friction pointing toward the center. Should a 'centripetal force' arrow be added?

Every arrow on a free-body diagram names a real force with an identifiable source.

No object exerts a separate 'centripetal force' on the bus; the inward job is already done by the friction shown.

No. The friction arrow already is the bus's centripetal force; adding another arrow would invent a force that does not act.

A space probe circles the Moon on a near-circular orbit. How many forces act on the probe?

Your turn

Which statement about centripetal force is correct?

Pavel lists the forces on a tin lunchbox whirling on a cord over smooth ice: the cord's tension, the lunchbox's weight, the ice's normal force, and a centripetal force. Which listed item is not a real force on the lunchbox?

A laundry cart rolls in a circle at a steady speed, steered by a curved guard rail. The cart's centripetal force is which of the following?