Angular momentum of a two-sided lever?
A pendulum is suspended at 1/3 of its length. It is in equilibrium. A ball of clay then hits the lower end of the pendulum.
You have to calculate the maximum angle of deflection. I know the principle of how this works (with a pendulum that is suspended at the highest point), but I don't know how to calculate the angular momentum in this case.
Do we consider only the part downstream of the suspension as the “lever arm”, i.e. L=2/3 * l X vBall, or the entire pendulum?
(1 votes)
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Before I present the solution for the pendulum with the 1/3 suspension here, I would like to experience how the maximum deflection angle is expected to be with a pendulum with the top suspension.
In my opinion, the determination of the rotational pulse is completely unnecessary. In my opinion, the energy conservation rate is completely different. The initial kinetic energy is.
This energy is then distributed in two potential energies. The potential energy of the staff
and the potential energy of the kneading ball
The deflection angle can thus be calculated.
And if the mass M of the pendulum and, instead, only the moment of inertia of the pendulum is known, the following representation also goes:
In no case is the observation of a rotary pulse necessary. Should the 1/3 suspension be calculated in this format?
Reason for the 2/3 suspension:
Energy conservation is not possible, is it? The ball has the speed v, about the common speed when the ball sticks to the pendulum nothing is known. That’s why I would have done it about the pulsation. I don’t know how to do that.
Sure. The kinetic energy is completely converted into the potential energy of pendulum and kneading ball itself. The kneading ball reaches a higher level. Just like the middle of the pendulum.
Yes. You can calculate the common speed if you wanted. For this, one would only have to know the moment of inertia of the pedel or to presuppose it as known with J_s. But this common speed is not in demand.
Rotary pulse maintenance is applicable when the kneading ball hits the pendulum. But after that, when the pendulum lifts, this rotational pulse is also completely absorbed up to the maximum deflection.
That is why I completely dispensed with the consideration of the rotational pulse. The energy conservation rate is enough. In order to calculate the maximum angle deflection, only the mass m of the kneading ball, its speed v and the moment of inertia J_s of the pendulum, or alternatively the length l and mass M the pendulum from which you could calculate the J_s. This method could also be used to calculate a 1/3 suspension. Do you want me?
Thank you:)
Added the calculation to the first answer. Just wanted to be sure someone was interested in it.
Thanks for the answer. But I don’t want to take your time now, if you want to make the calculation, I would be grateful to you:)