KE of Rotation & Moment of Inertia

AI Thread Summary
The discussion revolves around a physics problem involving a solid uniform cylinder and a stone tied to a string. The stone falls, and the participant calculates the angular velocity and kinetic energy of the cylinder. There is uncertainty about the mass of the cylinder, with one participant suggesting that the calculated mass of 30406 kg seems excessively large. The conversation highlights the importance of considering the kinetic energy of both the stone and the cylinder in the calculations. The participants are working collaboratively to verify the accuracy of the solution.
valeriex0x
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Homework Statement


A light string is wrapped around the outer rim of a solid uniform cylinder of diameter 75.0 cm that can rotate without friction about an axle through its center. A 3.00 kg stone is tied to the free end of the string, as shown in the figure . When the system is released from rest, you determine that the stone reaches a speed of 3.50 m/s after having fallen 2.50 m.

What is the mass of the cylinder?


Homework Equations



KE=1/2(1/2MR^2)ω^2

v=rω

The Attempt at a Solution



v=rw
3.50=.375w
w=9.3

ke=1/2(1/2M(.375)^2)(9.3)^2

I am doing this right and
is 30406kg correct?
 

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Hi again valeriex0x! :smile:

What did you do with the kinetic energy of the stone?

Btw, the mass you found looks a bit large doesn't it?
 
Last edited:
i got it
 
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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