Cylinder Falling from Unwinding String

AI Thread Summary
The discussion centers on a homework question involving a cylinder falling from an unwinding string, with the original poster seeking assistance. Participants emphasize the importance of demonstrating effort before receiving help, referencing forum rules. Suggestions include creating a diagram to visualize the problem and identifying relevant equations to connect the variables involved. The conversation highlights the need for a structured approach to problem-solving in physics. Engaging with the material through these steps is crucial for understanding the concepts.
milanocookie
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Homework Statement
Iron cylinder with radius r has a string wound around it. As cylinder falls it unwinds string. Write an equation that relates the forces that act on the cylinder to its linear accceleration a, along with an equation that relates the torques that act on the cylinder to its angular acceleration a.
Relevant Equations
Moment of inertia of a solid cylinder is I= ½mr²
I need help with this homework question and I'm blanking out. Can anyone help me to answer this question correctly.
 
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milanocookie said:
Can anyone help me to answer this question correctly.

Break it up in steps!

A good first step is to make a drawing that shows relevant variables

A natural second step is to collect relevant equations connecting these variables

##\ ##
 
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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