(II) Assume that a 1.00-kg ball is thrown solely by the action...

Question

(II) Assume that a 1.00-kg ball is thrown solely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 10–57. The ball is accelerated uniformly from rest to 8.5 m/s in 0.38 s, at which point it is released. Calculate
(a) the angular acceleration of the arm, and
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(a) the angular acceleration of the arm, and

Accepted Answer

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. What is the angular acceleration of the forearm when it propels a 1.50 kg apple from rest to 8.6 m per second in 0.39 seconds, solely through elbow rotation driven by the triceps muscle. So that's our angles. We're trying to figure out what the angular acceleration of the forearm is and that will be our final answer for this particular problem. So we're trying to figure out how, how, what the angular acceleration value is in order to for this person, a human to throw an apple, that's 1.5 kg from rest to 8.6 m per second in 0.39 seconds. Awesome. So let's quickly look at the diagram that's provided to us by the problem before we go and look at our multiple choice answers. As you can see, we have our forearm or we have an arm here. So we have our little bicep here at the very bottom of our figure. And then going up, we have the forearm and then we have our hand holding the apple. So then we have the triceps muscle, which is down in the lower bottom most part of our drawing. And then the axis of rotation at the elbow. As we can see, we have a red dot indicating the elbow and then an arrow pointing to the axis of rotation at the elbow. And then our triceps muscle, which is like when you go on, you flex your muscle, that's your tricep muscle. And we have an arrow pointing from that and that's at the bottom of our figure. And of course, the red circle in the hand is our apple. Awesome. So now that we have a visualization of this problem, let's look at our multiple choice answers to see what our final answer might be. Let us also quickly note that all of the units are in radians per second squared. So A is 43.19 B is 68.191 C is 70.11 and D is 99.11. OK. So, moving right along here. So first off, we need to recall and use the equation for angular velocity. And let's recall that the equation for angular velocity is omega. So Omega denotes angular velocity and Omega is equal to V divided by R where Omega of course is the angular velocity V is the linear velocity and R is the radius. We also need to recall and use the equation for angular acceleration. Let's call this equation too. So, angular acceleration states that alpha is equal to omega divided by T Awesome. Where of course alpha denotes the angular acceleration and T denotes time. And of course, we know that Omega is our angular velocity once again, Omega is angular velocity. OK. So now we need to substitute equation one into equation two. And when we do that, we will get that Omega or I'm sorry, uh alpha is equal to V divided by, are multiplied by T. So once again, we're substituting equation one into equation two. So we're taking the value for Omega in equation one and we're plugging it into equation two's value for Omega. That's how we get that alpha is equal to V divided by R multiplied by T. And let's call this equation three. So now at this point, we can substitute in all of our known variables into equation three to sol for the value of alpha, which is our angular acceleration in our final answer. So let us note that the value for V is given to us in the prom itself as 8.6 m per second because that's our velocity value that's provided to us by the prom itself. We're also told that the radius R is equal to 0.32 m. So 0.32 meters and we need to multiply it by 0.39 seconds. Is that how much time it takes for the Apple to get up to the speed? It needs to get to? Fantastic. So when you plug this equation into your calculator, you will find that it's equal to 68.91 radiance per second squared. Awesome. And that's it we've solved for this problem. Hooray, we did it. So looking at our multiple choice answers, it appears that our final answer has to be the letter B 68.91 radians per second square. And that is the angular acceleration of the arm. Thank you so much for watching. Hopefully, that helped and I can't wait to see you in the next video. Bye.

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