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1. The problem statement, all variables and given/known data

A smooth horizontal tube of lengthlrotates about a vertical axis. A particle placed at the extreme end of the tube is projected towards O(axis) with a velocitylωwhile 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]

2. Relevant equations

3. The attempt at a solution

Blurr at differential equation.

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# Homework Help: Centrifugal force

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