← Centripetal force

Tension does the job

A yo-yo whirls in a horizontal circle at the end of its string. An object in uniform circular motion always has a net force on it pointing toward the circle's center: its centripetal force. So some real force must be supplying the yo-yo's inward force. Which force is it?

Look at what touches the yo-yo: only the string. A stretched string exerts tension on whatever it holds, and tension acts along the string. Here the string runs from the yo-yo to the hand at the center.

The string runs from the yo-yo straight to the center of the circle. So the string's tension on the yo-yo points toward the center.

the handthe cordthe yo-yotension
The taut cord runs from the yo-yo to the center. Its tension points toward the center.

A net force toward the center is exactly what uniform circular motion requires. For the yo-yo, tension supplies the centripetal force.

Now the string goes slack. No tension acts on the yo-yo, and no force on the yo-yo points toward the center. With no net inward force, the yo-yo cannot keep moving in its circle.

the handthe yo-yothe cord hangs slack
The string goes slack. No tension acts, and no force points toward the center.

Now the string is taut again. Tension returns, pointing toward the center, and the yo-yo can circle again.

A dog runs in a circle at the end of a leash. The leash is a cord, stretched from the dog to its owner at the center. The leash's tension supplies the dog's centripetal force.

The pattern holds for any string, cord, rope, or wire: when the stretched cord runs from the circling object toward the center, the cord's tension is the inward force.

The test is one question: does a taut string, cord, or rope run from the object toward the circle's center? Yes means tension supplies the centripetal force.
One question decides each casecasetaut cord toward the center?what supplies the force?yo-yo, string tautyesthe string's tensionyo-yo, string slacknonothing: the circling cannot continuedog on a taut leashyesthe leash's tension
One question decides each case: does a taut cord run from the object toward the center?

A beanbag whirls in a horizontal circle on the end of a cord. Which force supplies the beanbag's centripetal force?

A key whirls in a horizontal circle on the end of its lanyard cord. Which force supplies the key's centripetal force?

Only the cord touches the key, and the cord is stretched.

The cord runs from the key to the hand at the circle's center, so its tension points toward the center.

The net force toward the center is the centripetal force.

The cord's tension supplies the key's centripetal force.

A skater grips a rope whose far end is tied to a post at the center of a rink, and glides in a circle around the post. Which force supplies the skater's centripetal force?

The rope is taut and runs from the skater to the post at the center.

So the rope's tension on the skater points toward the center of the circle.

The rope's tension supplies the skater's centripetal force.

A model airplane flies in a horizontal circle, held by a taut control line running to its pilot at the center. Nestor says: 'The line's tension supplies the plane's centripetal force.' Is he correct?

A horse circles its trainer at the end of a long taut rope. The rope's tension on the horse points in which direction?

Your turn

In which case does tension supply the centripetal force?

A sled whirls in a horizontal circle at the end of a taut rope on a frozen pond. Which force supplies the sled's centripetal force?

A ball is whirling in a horizontal circle on a string when the string suddenly goes slack. Which statement is correct?