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Simon Fraser University
University of Winnipeg
I) How much tension must a rope withstand if it is used to accelerate a 1210-kg car horizontally along a frictionless surface at 1.20 m/s$^2$ ?
(II) According to a simplified model of a mammalian heart, at each pulse approximately 20 $g$ of blood is accelerated from 0.25 m/s to 0.35 m/s during a period of 0.10 s. What is the magnitude of the force exerted by the heart muscle?
(I) A 7150-kg railroad car travels alone on a level frictionless track with a constant speed of 15.0 m/s. A 3350-kg load, initially at rest, is dropped onto the car. What will be the car's new speed?
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welcome to Unit eight, where we'll talk about rigid body rotation. So we're going to do a review here of the rotational Kinnah Matics that you may remember from earlier on. And then we'll move on to talk about forces dynamics, energy, momentum, all from the perspective of rotational motion instead of linear motion. So this unit is basically going to cover what the last several units have done for linear motion. But all in one go. So hopefully the similarities between the two will help you to be able to keep track of what's going on here and and keep up. Remember that as a quick review instead of using variables like X envy and they were gonna use variables like our or theta Omega and Alfa. Remember, the conversions we had here for s is equal to R theta. This is the arc length equation and we had tangential velocity is equal to our times omega and we had tangential acceleration was equal to our times. Alfa, where alphas angular acceleration and omega is angular velocity. We talked about other concepts like centripetal acceleration, which causes the rotation which is V t squared over our or omega squared are when you apply the conversion here. We also talked about centripetal forces, or centripetal force is equal mass times centripetal acceleration. But we didn't talk so much about tangential forces. We just said that there could be a tangential force which would cause a tangential acceleration here. Or as you could see here, putting in our times Alfa s. So this is more where we're going to focus on here is how does that work? And we're going to think about bodies freely rotating instead of having them fixed. Um, one interesting thought about rotational motion is if you consider an object and extended object rigid object in particular as it's going through the air. Generally, it has some sort of spiraling motion. So later on, this would rotate here and then here and then here and then here. Um And so if we really want to capture the motion of most physical objects, we need to think about the entire extended body, not just thinking about the body as a single point particle, as we have been in most cases before. Now eso really what we're trying to do is expand our mathematical model to include objects that have dimensions to them and are not just single point mass particles
Dynamics of Rotational Motion