(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An electric drill bit starts from rest and rotates with a constant angular acceleration. After the drill has rotated through a certain angle, the magnitude of the centripetal acceleration is twice the magnitude of the tangential acceleration. What is the angle?

2. Relevant equations

a_{c}=rw^{2}

a_{T}=r.angular acc

angular acc=(w-w_{0})/t-t_{0}

w=angular displacement/t

3. The attempt at a solution

a_{c}=2a_{t}

Therefore

rw^{2}=2r.angular acc

The radius cancels and therefore

w^{2}=2angular acc

=2(w-w_{0})/t

Given that the drill bit starts from rest, w_{0}=0 and therefore

w^{2}=2w/t

Divide throughout by w and we have

w=2/t

Sub w=angular displacment/t and we have

angular displacement/t=2/t

t cancels and we are left with

angular displacement=2 rads

This is not the answer given in the textbook, the answer is 1 rad

Please advise where I'm going wrong

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# Homework Help: Centripetal and Tangential Acceleration of drill bit

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