(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img340.imageshack.us/img340/7379/87835960.png [Broken]

[itex]r_{i}=.3 m \text{ and } r_{o}=.9 m[/itex]

The spool has a weight of 300N and a radius of gyration [itex]k_{O}[/itex] = .45 m. A cord is wrapped around its inner hub and the end subjected to a horizontal force P = 50N. Determine the spool's angular velocity in 4seconds starting from rest. Assume the spool rolls without slipping.

2. Relevant equations

[itex]\int_{0}^{t}{P\cdot r_{i}}{dt} = mv_{O}r_{i} + I_{O}\omega[/itex]

3. The attempt at a solution

[itex]\left \{ \begin{matrix}\int_{0}^{4}{50 \cdot 0.3}{dt} = \frac{300}{9.81}\cdot v_{O}\cdot0.9 + \frac{300}{9.81}\cdot 0.45^{2} \cdot \omega\\v_{O}=0.9\omega\end{matrix}[/itex]

Solving the two equations i get [itex]\omega = 1.94 \text{rad/s}[/itex]

The book provides the solution as follows

[itex]\left \{ \begin{matrix}

50(0.9 - 0.3)4 = \frac{300}{9.81}v_{O}\cdot 0.9+\frac{300}{9.81}\cdot.45^{2}\omega \\

v_{O}=\omega\cdot0.9 \end{matrix}[/itex]

I dont get why the book does .9 - .3 for its radius, i thought it was around point O?

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# Homework Help: Dynamics: planar kinetics of a rigid body (impulse and momentum)

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