Moment of Inertia Homework: Solving for Force P

AI Thread Summary
To solve for the force P acting on the rope wrapped around the hollow cylinder, the relationship between linear and angular velocity must be established using the equation v = ωr. The moment of inertia I can be calculated using I = MR², where M is the weight of the cylinder and R is its radius. The torque τ generated by the force P can be expressed as τ = P * R, and this relates to the angular acceleration α through the equation α = τ/I. By equating the work done by P to the change in kinetic energy of the cylinder, the value of P can be determined. Understanding these principles is crucial for solving the problem effectively.
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Homework Statement



A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 55.0 N and a radius of 0.25 m, that rotates without friction about a fixed horizontal axis. The cylinder is attached to the axle by spokes of a negligible moment of inertia. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 3.00 m, at which point the end of the rope is moving at 4.00 m/s. If the rope does not slip on the cylinder, what is the value of P?


Homework Equations



v=\omegar
\alpha=\tau/I
I=MR^2

The Attempt at a Solution



Alright, I honestly don't know where to start with this problem. It's review we're doing and I know the basics of inertia but nothing past that!

Can anybody help me start?

Thanks alot,
Peter
 
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work done by P on the cylinder = change in kinetic energy of the cylinder
 

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