Angular Impulse and Angular Momentum

AI Thread Summary
The discussion revolves around calculating the angular velocity (w) of an arm after a plug becomes wedged in a block, given various parameters like mass and distance. The user attempts to solve the problem using equations related to angular momentum and kinematics but finds their calculated w to be less than the expected 2 rad/s. They seek confirmation of their calculations and clarification on the significance of the 2 rad/s value. The conversation highlights the importance of accurately applying physics principles to solve for angular velocity in dynamic systems. The user is looking for guidance to ensure their approach is correct.
krnhseya
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Homework Statement



Mass of both end, distance from the pin point, height of the plug and its mass, angular velocity are given.
Need to fine angular velocity w of the arm immediately after plug has wedged itself in the block.

Homework Equations



(Ho)o = (Ho)horizontal

The Attempt at a Solution



1) 2(v1)(0.5) = (4+2)(0.5w)(0.5) + 6(0.3w)0.3
2) v^2 = vo^2 - 2g(y-yo) -> calculate v and substitute in v1

I find w to be a number smaller than 2 rad/s which is given and i know it's CW.
I just want to double check my work. thanks.
 
Last edited:
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if someone can guide me to right direction i'd really appreciate it. :)
 
whats the significance of 2 rad/s?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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