Centripetal Acceleration with infinite Radius?

AI Thread Summary
Centripetal acceleration is defined as the speed squared divided by the radius. When the radius approaches infinity, the centripetal acceleration approaches zero, as the formula v²/r indicates that an infinitely large radius results in an infinitely small acceleration. Although a finite radius, such as 40 km, would yield a non-zero centripetal acceleration, the specific case of an infinite radius leads to the conclusion that the centripetal acceleration is effectively zero. Thus, in this scenario, zero is the appropriate answer for centripetal acceleration with an infinite radius. The discussion emphasizes the mathematical interpretation of the relationship between speed and radius in centripetal motion.
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Centripetal Acceleration with infinite Radius??

Homework Statement



Find centripetal acceleration given speed is 38m/s and radius is infinity large




The Attempt at a Solution



So The answer would get infinitely smaller so is zero the best answer?
 
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I would say so, but usually even if it was considered infinitely large it would still have a centripetal acceleration e.g. r = 40 km.

However, how the question states it, r→ ∞ so v2/r → 0.
 

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