4. Angular Momentum & Rigid Bodies: The Billiard Ball Cue Strike Problem Statement A billiard ball of mass and radius
vx,cm=−L2sinθ⋅θ̇v sub x comma c m end-sub equals negative the fraction with numerator cap L and denominator 2 end-fraction sine theta center dot theta dot
Draw multiple, detailed diagrams (including FBDs). The coefficient of friction between the cylinder and
is placed inside the groove. The coefficient of friction between the cylinder and both walls of the groove is sufficiently large to prevent any slipping.
Determine the frequency of small oscillations of the cylinder about its equilibrium position. 4. Tips for Solving Competition Problems
This guide provides a collection of challenging mechanics problems, their detailed solutions, and links to top resources. 1. Top Recommended Resources: Problems with Solutions
you find hardest (e.g., rigid body collisions, fictitious forces, Lagrangian mechanics) rigid body collisions
d2Ueffdθ2|θ=π=−MgR−Mω2R2=−MR(g+ω2R)the fraction with numerator d squared cap U sub e f f end-sub and denominator d theta squared end-fraction vertical line sub theta equals pi end-sub equals negative cap M g cap R minus cap M omega squared cap R squared equals negative cap M cap R open paren g plus omega squared cap R close paren This value is always negative for any real , so the top position is always . Case 3: At the elevated angle ( ) Substitute into the second derivative formula:
Rigid body motion, angular momentum.
. Find the equilibrium positions of the bead and analyze their stability as a function of Step 1: Set up the Effective Potential
Kepler's Laws, potential, and kinetic energy of satellites. Oscillations: Harmonic motion, damping, and resonance. 4. Tips for Solving Competition Problems