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Mechanics
Mechanics

Centripetal Acceleration

ac=v2r=ω2ra_c = \frac{v^2}{r} = \omega^2 r

Acceleration pointing toward center of circular path.

Variables

a_c
Centripetal acceleration
Toward center
m/s²
v
Tangential velocity
Speed along circle
m/s
r
Radius
Radius of path
m
ω
Angular velocity
Rate of rotation
rad/s

Derivation

From geometry: a_c = v²/r. With v = ωr: a_c = ω²r.

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Common questions

What is the Centripetal Acceleration formula?

Centripetal Acceleration is written a_c = v²/r = ω² r. Acceleration pointing toward center of circular path. It belongs to Mechanics, under Rotational Motion.

What are the units in a_c = v²/r = ω² r?

In SI units, a_c is centripetal acceleration, measured in m/s²; v is tangential velocity, measured in m/s; r is radius, measured in m; ω is angular velocity, measured in rad/s.

How is the Centripetal Acceleration formula derived?

From geometry: a_c = v²/r. With v = ωr: a_c = ω²r. The result is a_c = v²/r = ω² r.