Review the key concepts, equations, and skills for centripetal motion, including intuition for the direction of centripetal acceleration.

Key terms

Term (symbol)Meaning
Centripetal acceleration (aca_c)Acceleration pointed towards the center of a curved path and perpendicular to the object’s velocity. Causes an object to change its direction and not its speed along a circular pathway. Also called radial acceleration. SI units are ms2\dfrac{\text m}{\text s^2}.

Equations

EquationSymbol breakdownMeaning in words
ac=v2ra_c = \dfrac{v^2}{r}aca_c is radial acceleration, vv is linear speed, and rr is radius of the circleRadial acceleration is directly proportional to the square of the linear speed and inversely proportional to the radius of the curved pathway.
ac=ω2ra_c = \omega ^2raca_c is radial acceleration, ω\omega is angular speed, and rr is radius of the circleRadial acceleration is directly proportional to the product of the square of the angular speed and the radius of the curved pathway.

Common mistakes and misconceptions

People mistakenly think centripetal acceleration points tangentially outwards. Acceleration is the velocity change per time. Objects in uniform circular motion move along a circular pathway at constant speed, so acceleration can only point perpendicular to the velocity for a change in direction only.
The acceleration vector must point inward toward the center to turn the object back onto the circular path. An outward acceleration would turn the object’s direction out and away from the circular path. For more insight to the direction of acceleration and velocity for uniform circular motion, watch our video about how centripetal acceleration relates to velocity and radius.
One way to keep track of the direction is to remember that CENTripetal acceleration points to the CENTer of the object’s curved path.

Learn more

For deeper explanations of centripetal acceleration, see our video about race cars with constant speed around curves.
To check your understanding and work toward mastering these concepts, check out the exercise on predicting changes in centripetal acceleration.
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