$2-9.$ An airplane flies with a constant speed $v$ in a level turn to the left at a constant

radius $R.$ The propeiler is of radius $r$ and rotates about its axis in a clockwise sense

$64$

Kinematics of a Particle

Chapter $2$

$($as viewed from the rear$)$ with a constant angular velocity $.$ Find the total acceleration of a point $P$ at the tip of the propeller, assuming that its axis is always aligned with the flight path. Use cylindrical unit vectors and assume that the velocity of $P$ relative to the airplane is vertically upward at $t=0.$