How Does a Clay Ball Impact the Rotation Angle of a Rod?

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Homework Help Overview

The problem involves a 75 kg rod and a 10 kg clay ball impacting its rotation. The scenario describes the rod hanging vertically and the clay ball traveling horizontally before colliding with the rod's tip. The goal is to determine the maximum angle of rotation from the vertical after the collision.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss calculating the moment of inertia for both the rod and the clay ball, with one participant expressing uncertainty about the next steps after this calculation. Questions are raised regarding the momentum of the clay ball and its relation to the moment of momentum on the rod.

Discussion Status

Some participants have provided guidance on considering the momentum and angular momentum in the system. There is exploration of the relationship between moment of inertia, angular velocity, and momentum. Multiple interpretations of the problem are being discussed, but there is no explicit consensus on the approach to take.

Contextual Notes

Participants are working with the assumption that the rod is frictionless and that the clay ball sticks upon impact. There is mention of kinetic energy being converted to potential energy, but the specific formulas and methods for solving for the angle are not fully established.

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Homework Statement



A 75kg, 30 cm long rod hangs vertically on a frictionless, horizontal axle that passes through its centre. A 10kg ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very bottom tip of the rod.
To what maximum angle (measured from the vertical) does the rod (with the clay ball attached) rotate?

Homework Equations





The Attempt at a Solution



Not sure where to start on this, apart from calculating the moment of inertia for the rod and for the ball and adding them together to get a total inertia?
From there, I have no clue.
 
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Hi Shannon12, welcome to PF.
What is the momentum of of the clay ball? What is the moment of momentum on the rod?
What is the relation between moment of inertia, angular velocity and momentum of momentum?
 
rl.bhat said:
Hi Shannon12, welcome to PF.
What is the momentum of of the clay ball? What is the moment of momentum on the rod?
What is the relation between moment of inertia, angular velocity and momentum of momentum?


Thank-you! :D
Umm ok so momentum = mv = 0.01 x 2.5 = 0.25 kg m^-1 s^-1 for the clay ball
And the momentum of the rod is I = 1/12 mL^2 = 1/12 (0.075)(0.3^2) = 5.625 E-4

For the second part, I'm not too certain. Í tried checking my book to see if there were any formulas but I couldn't find one..
 
Moment of the mud ball produces the angular momentum in the (rod+ mud ball) sustem.
So mv*L/2 = I*ω. Due to the angular velocity the system acquires kinetic energy. When the system comes to rest KE is converted to PE.
So 1/2*I*ω^2 = mgh = mgL/2(1 - cosθ)
Solve for θ.
 

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