- #1

toesockshoe

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## Homework Statement

A stick of length L and mass M is in free space and not rotating. A point mass m has an initial velocity v heading in a trajectory perpendicular to the stick. The mass collides and adheres to the stick a distance b from the center of the stick. Find the resulting motion of the two together in terms of their center of mass velocity and final angular velocity.

## Homework Equations

L=IW

L=rxp

## The Attempt at a Solution

I set the origin at the center of rotation (in the middle of the stick)

LET M STAND FOR THE SMALL MASS AND S STAND FOR THE STICK.

this is a momentum problem so i said [itex] L_i=L_f [/itex] at the time of contact.

[itex] L_{mi} + L_{si} =

**L_{mf} + L_{sf} [/itex]**

initial momentm of the stick is 0.

[itex] mv_ib = I_{stick}w+I_{mass}w [/itex]

[itex] m_pv_ib=\frac{m_sL^2}{12}w_f + mb^2w [/itex]

solve for [itex] w_f [/itex]

[itex] w_f = \frac{m_pv_ib}{\frac{mL^2}{12}+m_pb^2} [/itex]

initial momentm of the stick is 0.

[itex] mv_ib = I_{stick}w+I_{mass}w [/itex]

[itex] m_pv_ib=\frac{m_sL^2}{12}w_f + mb^2w [/itex]

solve for [itex] w_f [/itex]

[itex] w_f = \frac{m_pv_ib}{\frac{mL^2}{12}+m_pb^2} [/itex]

i know i didnt solve for center of mass velocity but would we just do a regular momentum problem? (not rotational) becasue there are no external forces and the center of mass wouldn't really be affected by the rotations right? [/B]