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Eugene Hecht

12 Edition

Chapter 10, Problem 13

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The moment of inertia of the frictionless pulley system illustrated in $\underline{\text { Fig. } 10-4}$ is $I=1.70 \mathrm{~kg} \cdot \mathrm{m}^{2}$, where $r_{1}=50 \mathrm{~cm}$ and $r_{2}=20 \mathrm{~cm}$.Find the angular acceleration of the pulley system and the tensions $F_{T 1}$ and $F_{T 2}$.

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Transcript

Hi this question, given that the moment of inertia I is 1.7 kilogram meters. Good. And reduce our one here is 50 cm and that is a call to Divided by 100, I’ll be served by five m. There are two strength is something he does. Should we go to job or two does? Excuse me. Won’t find the uncle acceleration police system. So And we also don’t find detentions ft one and 52. So first of all it’s gonna do it force the net force on this to kill grandmas so on to kill grandma A physical to EMI from Newton’s 2nd. And the net force F will be to force the weight pulling downwards so they will be empty. She is two times 2 times nine x 8 minus the fictional force to the detention of force which is upward so the opposite direction. Just be subtracted -51 physical to M. A. And we can substitute she ate it comes to Times nine. It’s 1 mhm -51. It’s called to M. A two times the acceleration he Oxidation of the side which will be a one. Yeah. And they went here, Yeah, she has one equation and then for one, the equation for the that force are on the side what can you have 1.8 same same idea here. But this time the only the expression is going up and the assertion is is in the same direction as the the tension force. We’re going to do the tension force minus the MG. So this pFT to manage MG because they’re me. So at 1.8 times. So sir, this should not be 52 FY 2 -1.8. Chapter nine Point It’s one Physical to one point it it suits. So now we have two equations and also we can do the talk around this side. So the talk here, it’s going to be pulling it this way. You talk as a result of this and it’s all kind of result. Otis says it’s pulling the sweet clockwise anti clockwise so we can call this side Talk one and just talk to. Yeah. And know…