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Amio

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I am reading introductory physics from Serway. Where they say

But aren't the radial and centripetal acceleration same (correct me if I am wrong)? Why is there a minus sign?

The book explains by saying that

I don't understand this explanation because as the direction of the radial acceleration is also towards the center, shouldn't it be [tex] a_{radial} = a_{centripetal} ?[/tex] Why the minus sign?

Would someone please clarify?

**if [tex] a_r [/tex] is radial acceleration and [tex] a_c [/tex] is centripetal acceleration then [tex] a_c = v^2/r [/tex] and [tex] a_r = -a_c = - v^2/r [/tex]**But aren't the radial and centripetal acceleration same (correct me if I am wrong)? Why is there a minus sign?

The book explains by saying that

**the negative sign indicates that the direction of centripetal acceleration is towards the center of the circle representing the radius of curvature.**.I don't understand this explanation because as the direction of the radial acceleration is also towards the center, shouldn't it be [tex] a_{radial} = a_{centripetal} ?[/tex] Why the minus sign?

Would someone please clarify?

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