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In the figure above, what is the torque about the pendulum's suspension point produced by the weight of the bob, given that the length of the pendulum, $L,$ is 80 $\mathrm{cm}$ and $m=0.50 \mathrm{kg} ?$(A) 0.5 $\mathrm{N} \cdot \mathrm{m}$(B) 1.0 $\mathrm{N} \cdot \mathrm{m}$(C) 1.7 $\mathrm{N} \cdot \mathrm{m}$(D) 2.0 $\mathrm{N} \cdot \mathrm{m}$

Physics 101 Mechanics

Chapter 7

Uniform Circular Motion, Newton’s Law of Gravitation, and Rotational Motion

Gravitation

Dynamics of Rotational Motion

University of Michigan - Ann Arbor

University of Washington

Hope College

University of Winnipeg

Lectures

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in the figure above. What is the torque about the pendulum suspension point produced by the way to the Bob, Given that the length of the pendulum l is 80 centimeters and em is equal to 0.50 kilograms. Okay, so this is Ah, pretty standard AP Physics one Multiple choice question. And just like any multiple choice Question. I need a bucket. The question I need to know. Okay. Is this a force question? Is this an energy question? Waves. Ah, What? What kind of what type of question is this? And there's one word in the question that is a dead giveaway as to what kind of question that is. And that is the word torque. So we know that this is going to be a torque question. And so we need to look at our AP physics equation sheet for Okay. What? What is the equation for torque? Well, if we look there, it will say torque is equal to our perpendicular if Okay, so that means Ah, like all three of these quantities air vectors. So we're gonna put vector hats over the top. The vector, remember, has both magnitude and direction. So the directions of our vectors are very important when it comes to torque, because what this perpendicular sign means here is I only want the amount of force that is perpendicular to the our vector to calculate torque. Because if, ah, if there's some force that is parallel to the our vector, well, that's not gonna affect the torque. It's still a force, but it's not a torque. I only want the amount of force that is causing a torque, and that's gonna be perpendicular to the our vector. There's another equation that you'll see on your equation sheet for torque, and that is our if sign Fada. And so this is what we're going to use to actually calculate the answer once we kind of get our bearings of what's going on with our vectors. So really, the tough part of this problem has to do with vectors in and of themselves and some angle things, Um, not really the calculations in and of themselves. So let's let's look at our vector. So I'm going to scroll down here. I have a picture here if my people will do it. Okay, there we go. So I got a separate picture here of the actual set up, and we're going to draw all over this. Okay, So what's going on here is we first need to find our our our vector. So we want to find the are vector, and then I want to find the f vector. So what is actually causing the force? The force vector will be very easy to find. In fact, we'll just label it right now. Ah, for a pendulum, the only external force that's acting on the pendulum is the force of gravity on the bob itself. So we're just gonna label f g right here. That is our force vector. It is in the negative y direction. It's straight downward now for our vector. The are vector is a line. The direction, at least, is a line connecting two points. The point about which were rotating, which is appear and the point of where the forces actually acting, which is down here. So I want to make a straight line a straight as I can. I'm going to extend it beyond a little bit. Now. The length of my our vector is just from here to here because ah, that's the length of the pendulum itself. But just for demonstration purposes so we can see the entire length of the vector. The direction of the vector keeps going and going, even though the length stops at a certain point. So this is going to be my our vector. And ah, this is very important because this data up here, this data is between both the are vector and the effect er So if we go back down here, what we can see is that the angle between the are vector and F vector is actually right. No, that's not what I want. I want that is right here. That's the angle that we're looking for. This is the fada that we want. That's the data that we want for our, um, for our equation now were given an angle. We have this angle right here, but this angle and that angle are not the same. If you'll remember back to your love, alternate into your angles. Those air Not gonna be the same eso If I can draw a horizontal line going through here, the 60 degrees would actually be right here. That's where that's where that 60 goes. Eso this fado that were actually looking for is going to be 90 minus 60 90 minus 60 because FG is in the negative y direction and then we have our black whores on the line here, which is in the X direction. So that's 90 degrees between there. We know that 60 degrees of that is found right here, so that means the rest of it has to be right here. 90 minus 60 obviously is 30 degrees. So the angle between our our vector and R F Victor is 30 degrees. And that's really important that you get the right angle, because if you put in 60 into the sine function, it's not You're not gonna get the right answer. So AP likes to do that a lot, so just make sure that you know exactly what angle you are looking at. So now we can come back up to here now that we know that our angle that we're looking at is 30 degrees. Now that we know that fate A is equal to 30 degrees, now we can calculate the the magnitude of everything else. So the, um the are vector is just ah, the length of that vector is just l which is 80 centimeters and when you need to put that into S I units which is going to be meters. So we have 0.80 meters after we convert that and then we're gonna find the magnitude of R f Victor. So our F vector is just f g, which is equal to M times G. We know and love this equation. So where mass is half of a kilogram and RG is 10. Remember for AP physics multiple choice questions We can approximate g to be 10 meters per second squared eso when we plugged that into our calculator will end up getting 5.0 Newtons So now we're good to go to ah couch to find our answer So we're gonna plug all of our numbers in So I want I want that So Tao is going to be equal to our which is, um, 0.80 times R f victor, which is 5.0 times the sign of fada, which is 30. Plug all that into your calculator and you will get 2.0 Newton meters. So our answer here is de

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