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**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