A particle of mass m slides down a frictionless surface through a height h and collides with a uniform vertical rod (of mass M and lenght d), sticking to it. The rod pivots about point O through an angle before momentarily stopping. Find the angle.(adsbygoogle = window.adsbygoogle || []).push({});

Now, I can find the tangential velocity of the particle when it hits the rod, and therefore, its omega. After this I just have absolutely no idea where to go with it. I'm assuming there is no friction between the rod and point O, and that the only force stopping this rod from continuing to spin around is gravity. I tried to say g = alpha * d but then thought gravity wasnt tangential at all points so it's not valid. It doesn't say whether the collision is elastic or inelastic, so I'm assuming inelastic. Momentum must be conserved, so at the collision, mrv = (Irod+Iparticle)(omega), but that won't tell me when it stops. Then I thought that perhaps the circumference through which the rod-particle system moves is h, so h=(theta)*d [arc length], but that's not right either.

I have a feeling a torque may be involved here, but that could only give me an alpha not a theta.

If anyone is willing to do it out it says the correct answer is arccos[ 1 - (6m^2h)/(d(2m+M)(3m+M))], but I have no idea where that could even come from. I don't recognize any parts of it.

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# Particle slides into a rod and pivots

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