- #1

Zinggy

- 12

- 0

## Homework Statement

A small bead of mass m slides on a frictionless cylinder of radius R which lies with its cylindrical axis horizontal. At t = 0 , when the bead is at (R,0), v

_{z}= 0 and the bead has an initial angular momentum L

_{o}< mR sqrt(Rg) about the axis of the cylinder where g is the acceleration due to gravity. The bead slides from (R,0) down the curved surface of the cylinder and eventually loses contact with that surface.

2. Homework Equations

*Find r(double dot) in Cylindrical Coordinates.*2. Homework Equations

Position Vector of r = ˆ iRcosφ + ˆ jRsinφ = ρˆR

## The Attempt at a Solution

I know r(double dot) is the same as d

^{2}r/dt

^{2}so;

r = ˆ iRcosφ + ˆ jRsinφ = ρˆR

r(dot) =- iRsinφ+jRcosφ -unless R changes with time, which I don't think it does.

then

r(double dot) = iR-cosφ - jRsinφ

I think I'm missing something. Do I need to include the angular momentum somewhere?