In a charming 19th century hotel an old style elevator is...

In a charming 19th-century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 2.50 m in diameter (Figure 1). The elevator is raised and lowered by turning the disk, and the cable does not slip on the rim of the disk but turns with it.

Transcript

00:01 Okay, so imagine that there's an elevator connected to a wire connected to a disk.

00:09 Okay, so we know that the disk has the diameter of 2 .5, which means that the radius of the disk is 1 .25 meters.

00:23 So the first question it asked for what is the revolution per minute of the disk so that it maintains a constant? 25 centimeters per second of lifting this elevator up.

00:39 So it's gonna be 0 .25 meters per second by the way.

00:43 Okay, so one thing we need to understand is that when this elevated, when this block is moving up a constant rate of 0 .25 meters per second, then the outermost of this, this is also rotating at the same speed.

01:04 Okay, so first of all, i want to say that there are many ways to approach this problem, but personally for me, i'd like to do it this way.

01:15 Okay, so this is just me setting up a proportion.

01:21 So why do i set a proportion? so if the rate of rotation of the disk per second, that it corresponds to this one, then after a whole minute, the rotation per minute is going to correspond to how high the elevator has traveled up in one minute.

01:49 Okay, so the question here is that how much has the elevator traveled up in 60 seconds? so when it has traveled up 60 seconds, then it's 25 centimeter times 60, we should get 15 meters total.

02:27 Total rise.

02:29 It's 15 meter.

02:31 Okay, so the disk has to rotate 15 meters from the starting point.

02:39 So if this disk was, has a circumvent.

02:42 Of 3, then it has to rotate 15 meters.

02:49 So it has to rotate five rounds.

02:53 So what we can do is from that, we can say that, oh, the revolution per minute is equal to the total rise of the elevator divided by the circumference of the disk.

03:10 So 15 meters divided by 2 pi r our radius which is 1 .25.

03:20 So 15 divided by 2 .5 times pi, we should get 15 divided by 2 .5 pi.

03:30 We should get 15 divided by 2 .5 pi.

03:36 That's going to be equal to 1 .9 revolution per minute.

03:45 And that's our first answer.

03:51 For a.

03:52 So now we're gonna move on to b.

03:57 So what's the angular acceleration? okay, now we know that the linear acceleration is going to be equal to the angular acceleration times the radius.

04:12 And so therefore manipulating this equation here, we divide both sides by r.

04:19 These are they cancel out...

Question

In a charming 19th-century hotel, an old-style elevator is connected to a counterweight by a cable that passes over a rotating disk 2.50 m in diameter (Figure 1). The elevator is raised and lowered by turning the disk, and the cable does not slip on the rim of the disk but turns with it.

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