A 4 m long blade initially at rest begins to spin with 3 rad/s 2 around its axis, which is located at the middle of the blade. It accelerates for 10 s. Find the tangential speed of a point at the tip of the blade 10 s after it starts rotating.

Alright. So here we have a 4 meter long blade that's initially at rest. So let me draw a little blade here. And the length of the blade, so from side to side is 4 meters. Okay. It's initially at rest. So mega initial equals 0 And it rotates. It begins to spin with alpha of 3. I know it's alpha because it's radians per second squared. And it does this around its axis, which is located in the middle of the blade. So the idea here is that the blade spins around this point. Much like a helicopter blade, you have half of the blade, to the left of the center, the other half to the right, and you're going to rotate around the middle here. Okay. It does this for 10 seconds and we wanna know the tangential speed of a point at the tip of the blade. So imagine a point right here and I wanna to know what is v t of that point. Okay? It accelerates for 10 seconds and I want to know what is v t after those 10 seconds. All right? Now remember, the tangential velocity of a point that goes around the circle is given by v t equals r omega. Now what should we use as r? Well, r is the distance from the center. And the center is in the middle of this object. So the r is this. It's not the full 4 meters, but it's half of that because you're at the edge. So it's 2 meters. So we got the r figured out. What about omega? We don't have omega, but we can use the fact that we have 3 variables of motion here, 3 motion variables to find our omega. So this is after 10 seconds. So I want to know Omega final. Okay? I know 3 out of 5 variables already. So that means I can solve the 5th variable that's not here is Delta Theta. That's the ignored variable and that tells us that we're supposed to use the first equation. So it's going to be very straightforward. Omega final equals Omega initial plus alpha t. This is 0. Alpha is 3. T is 10. So this is 30. Now we're ready to plug it in here. R is 2 not 4. This is 30. So you get 60 meters per second. I know it's meters per second because the, the variable is velocity v. Okay? That's it for this one. There's nothing weird in this question. Very straightforward. The only sort of weird thing was the fact that the r is half of the length because we're talking about a blade that spins around its own central axis. Okay? That's it for this one. Let me know if you guys have any questions.

Physics with Algebra 때문에 힘들어하고 계신가요?

A 4 m long blade initially at rest begins to spin with 3 rad/s2 around its axis, which is located at the middle of the blade. It accelerates for 10 s. Find the tangential speed of a point at the tip of the blade 10 s after it starts rotating.

다음 시청

A 4 m long blade initially at rest begins to spin with 3 rad/s² around its axis, which is located at the middle of the blade. It accelerates for 10 s. Find the tangential speed of a point at the tip of the blade 10 s after it starts rotating.