Question

RSES/ph222/W1 HW.pdf WI An electric drill 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 of a point on the drill is twice the magnitude of the tangential acceleration. What is the angle?

Answer 1

given

a_c = 2a_t

where c is for centripetal and t is for tangential

a_c = rw²

a_t = r$\alpha$

rw² = 2r$\alpha$

w² = 2$\alpha$

Using rotation kinematics, we have

2$\alpha$ = 2$\alpha$*$\Delta \theta$

$\Delta \theta$ = 1 rad