Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_147

2/147 The particle \( P \) moves down the spiral path which is wrapped around the surface of a right circular cone of base radius \( b \) and altitude \( h \). The angle \( \gamma \) between the tangent to the curve at any point and a horizontal tangent to the cone at this point is constant. Also the motion of the particle is controlled so that \( \dot{\theta} \) is constant. Determine the expression for the radial acceleration \( a_r \) of the particle for any value of \( \theta \).