Centripetal and Tangential Acceleration of drill bit

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
ac=rw2
aT=r.angular acc
angular acc=(w-w0)/t-t0
w=angular displacement/t

3. The attempt at a solution
ac=2at
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

Homework Helper
3,055
4
Consider that ω2r is your Centripetal acceleration.

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

You know from kinematics that ωf2 = ωi2 + 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
 

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