Formulas & tables/Physics/Dynamics/Centripetal force

Centripetal force

Fd=mv2r=mω2rF_d=\dfrac{mv^2}{r}=m\omega^2 r

Result unit: N (newton)

What it describes

A force directed toward the centre of the circle, keeping the body on its circular path.

Symbols

FdF_d
centripetal force
[N]
mm
mass
[kg]
vv
linear velocity
[m/s]
rr
radius of the path
[m]
ω\omega
angular velocity
[rad/s]

Where it comes from

A body in circular motion constantly changes the direction of its velocity — this requires a force directed toward the centre. It is not a separate force, but a role played by, for example, friction, the tension of a rope or gravity.

When to use it

Circular motion — bends, orbits, centrifuges. Equivalently Fd=mω2rF_d=m\omega^2 r.

Example

A 0.5 kg body moves in a circle of radius r=2r=2 m at a speed of 4 m/s. Find the centripetal force.
Substitutionm=0.5m=0.5 kg, v=4v=4 m/s, r=2r=2 m.
ResultFd=0.5⋅422=4F_d=\dfrac{0.5\cdot4^2}{2}=4 N.

Related formulas

Linear velocity in circular motion Newton's law of universal gravitation

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