- #1

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**"Centrifugal force"**

## Homework Statement

A smooth horizontal tube of length

*l*rotates about a vertical axis. A particle placed at the extreme end of the tube is projected towards O(axis) with a velocity

*lω*while at the same time the tube rotates about the axis with constant angular speed ω. Determine the path.

Solution

The only force on the particle is the inertial force("Centrifugal force")

*mrω*

^{2}Newton's second law becomes

[itex]m\ddot r=0+mrw^2 \ or \ \ddot r=ω^2r [/itex]

This part I don't understand

[itex]Multiplying\ by\ \dot r dt=dr \ \ and\ integrating [/itex]

[itex]\frac {1}{2}\int d(\dot r)^2=w^2 \int rdr [/itex]

[itex]\frac {1}{2}(\dot r)^2=\frac {1}{2}w^2 r^2 + c [/itex]

## Homework Equations

## The Attempt at a Solution

Blurr at differential equation.