Mass needed to rotate wheel and axle (rotational motion)

AI Thread Summary
To determine how far a mass must fall to achieve a rotational rate of 3 rev/s for a wheel and axle with a total moment of inertia of 0.002 kgm, energy conservation principles are applied. The potential energy of the falling mass converts into both the rotational kinetic energy of the axle and the kinetic energy of the mass itself. The relationship between linear velocity and angular velocity is utilized, where v = wr, to find the mass's velocity when the wheel reaches the desired rotational speed. The discussion emphasizes understanding the concepts rather than simply providing answers, fostering a deeper grasp of the problem. Ultimately, the participant successfully comprehends the solution through this collaborative approach.
MinaHany
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I'm sorry for posting another thread but I'm totally lost here..

Homework Statement


A wheel and axle having a totel moment of inertia of 0.002kgm is caused to rotate about a horizontal axis by means of an 800g mass attached to a cord wrapped around the axle.
The radius of the axle is 2cm. Starting from rest, how far must the mass fall to give the wheel a rotational rate of 3rev/s?
 
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Use energy. Spinning the wheel and axle combo will impart a kinetic energy. The falling mass will have kinetic energy. The state of the system before the mass falls relies on its (the mass) potential energy. Since the mass is attached to the axle, you know that the kinetic energy of the spinning axle and the falling mass are somehow tied together. How so? From there, conservation of energy is your answer. You know the rotational speed of the axle in the final state.
 
Thank you sethric..
I wrote that final KE = inital KE
rotational KE + KE of the mass = PE of the mass

and v=wr to get the v of the mass when the w is 3 rev/s

Best thing around here is nobody gives the answer.. everybody gives you the ideas you need to understand to be able to solve the problem.

I understand it now.. Thanks again.
 
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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