Centripetal Force Formula

Centripetal force is the net inward force required to keep an object moving along a circular path, directed toward the centre of the circle, equal to.

The Formula

F=mv2rF = \frac{mv^2}{r} (mass times velocity squared divided by radius)

When to use: The force that pulls you toward the center when you go around a curve.

Quick Example

A string pulling on a ball you're swinging, friction on car tires in a turn.

Notation

FcF_c is centripetal force in newtons, mm is mass in kg, vv is tangential speed in m/s, rr is the radius of the circular path in metres, and ω\omega is angular velocity in rad/s.

What This Formula Means

The net inward force required to keep an object moving along a circular path, directed toward the centre of the circle, equal to mv2/rmv^2/r where mm is the object's mass, vv its speed, and rr the radius of the circle.

The force that pulls you toward the center when you go around a curve.

Formal View

For uniform circular motion, the net radial force is Fc=mv2r=mω2rF_c = \frac{mv^2}{r} = m\omega^2 r, directed toward the centre of the circular path. This force produces centripetal acceleration ac=v2/ra_c = v^2/r.

Worked Examples

Example 1

medium
A 0.5 kg0.5 \text{ kg} ball on a 1.2 m1.2 \text{ m} string is swung in a horizontal circle at 4 m/s4 \text{ m/s}. What is the centripetal force?

Answer

Fc≈6.67 NF_c \approx 6.67 \text{ N}

First step

1
Recall the centripetal force formula: Fc=mv2rF_c = \frac{mv^2}{r}, where mm is mass, vv is speed, and rr is radius.

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Example 2

hard
A car of mass 1000 kg1000 \text{ kg} rounds a curve of radius 50 m50 \text{ m}. If the maximum static friction force is 8000 N8000 \text{ N}, what is the maximum safe speed?

Example 3

medium
A 1200 kg1200\text{ kg} car rounds a flat curve of radius 80 m80\text{ m} at 20 m/s20\text{ m/s}. What friction force keeps it on the curve?

Common Mistakes

  • Treating centripetal force as a separate, additional force in a free-body diagram — it is the net result of real forces (tension, gravity, friction) directed toward the centre. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Confusing centripetal force (real, inward) with centrifugal force (fictitious, outward) — centrifugal force only appears in rotating reference frames. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Forgetting that speed must be squared in F=mv2/rF = mv^2/r — doubling the speed quadruples the required centripetal force. - Fix this by naming the system, checking "Have I isolated one system and listed the external forces or torques acting on it before applying a law?", and attaching units or direction to the final statement.
  • Using centripetal force from a keyword alone - Signal words like force, push, pull only point to a possible model; the system must match too.

Why This Formula Matters

Centripetal Force is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

Frequently Asked Questions

What is the Centripetal Force formula?

The net inward force required to keep an object moving along a circular path, directed toward the centre of the circle, equal to mv2/rmv^2/r where mm is the object's mass, vv its speed, and rr the radius of the circle.

How do you use the Centripetal Force formula?

The force that pulls you toward the center when you go around a curve.

What do the symbols mean in the Centripetal Force formula?

FcF_c is centripetal force in newtons, mm is mass in kg, vv is tangential speed in m/s, rr is the radius of the circular path in metres, and ω\omega is angular velocity in rad/s.

Why is the Centripetal Force formula important in Physics?

Centripetal Force is central because forces explain changes in motion and balance. Students who can isolate a system and draw the interactions can avoid treating every force word as the same kind of cause.

What do students get wrong about Centripetal Force?

Students often know a formula related to centripetal force but skip the recognition step: Have I isolated one system and listed the external forces or torques acting on it before applying a law? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Centripetal Force formula?

Before studying the Centripetal Force formula, you should understand: circular motion, force.

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