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lizzyb
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Homework Statement
A wad of sticky clay (mass m, velocity v), is fired at a solid cylinder (mass M, radius R). The cylinder is initially at rest and rotates on an axis through the center of mass. The line of motion of the projectile is perpendicular to the axis of rotation and at a distance d < R from the center.
Find the angular speed of the cylinder just as the clay hits the surface.
Homework Equations
Conservation of Angular Momentum
See: https://www.physicsforums.com/showthread.php?t=63404
The Attempt at a Solution
I did:
[tex]L_i = d m v_i[/tex]
[tex]L_f = d m v_f + \frac{1}{2} M r^2 \omega = d m r \omega + \frac{1}{2} M r^2[/tex]
[tex]L_i = L_f [/tex]
[tex]d m v_i = d m r \omega + \frac{1}{2} M r^2 \omega[/tex]
[tex] \omega = \frac{d m v_i}{(d m r + \frac{M r^2}{2})}[/tex]
Which isn't correct; it may have something to do with the momentum of the wad of sticky clay; the reason I used L = m v d is because d would be the moment arm but perhaps I'm confusing this with torque? What value of r should I use when the force isn't perpindicular?