Centripetal and Tangential Acceleration of drill bit

[invadertak]

Homework Statement

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?

Homework Equations

a_c=rw²
a_T=r.angular acc
angular acc=(w-w₀)/t-t₀
w=angular displacement/t

The Attempt at a Solution

a_c=2a_t
Therefore
rw²=2r.angular acc
The radius cancels and therefore
w²=2angular acc
=2(w-w₀)/t
Given that the drill bit starts from rest, w₀=0 and therefore
w²=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

 

[LowlyPion]

Consider that ω²r is your Centripetal acceleration.

And that your Tangential acceleration is a = α*r.

You know from kinematics that ω_f² = ω_i² + 2*α*θ or since there is no initial ω :

ω² = 2*α*θ

So ... for the given that

ω²*r = 2*α*r

Substitute for ω²