12. Rotational Kinematics

Converting Between Linear & Rotational

# Anderson Video - Spinning Ice Skater

Professor Anderson

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>> Hello class. Let's take a look at a problem that might have relevance to your homework. This is a problem of an ice skater spinning. And let's take a top view picture of this ice skater. And so, here is Brian Boitano's head and there are his hands. Kind of really ridiculously large hands, but that's okay. And he's spinning. Okay and he's going around like this. And let's say that he is spinning at 100 RPM. Okay, which ice skaters can do. Right? They can spin at 100 RPM. Let's calculate the speed of Brian Boitano's hands as he spins. And we're going to approximate this length here. The length of his arm as 70 centimeters. Okay, and let's ask this question. What is the speed of the hand? Okay. How do we do that? Well, first off, we realize that there's a nice relationship between V and omega. And the relationship is this, V is equal to omega times R. Okay, so if something is spinning in a circle, how fast is it moving? It depends on omega and it depends on the radius, R. So, we don't really have omega yet. But we do know that we have 100 RPM. A hundred RMPs is 100 revolutions per minute. But we know that omega has got to be in radians per second. So, first off, we've got to get rid of the minutes. So, we multiply by 1, we put 1 minute up there, 60 seconds down there. And then we've got to get rid of the revs. Revs is a unit-less quantity of course, but we need to get rid of it. and we remember that one revolution, one all the way around is what? >> (student speaking) Two pi. >> Two pi. Two pi radians. Okay, so we just multiplied by 1 every time, we've just changed the units. And now we can cross out some stuff. Revs cancels with rev. Minutes cancels with minutes. And we get 100 times 2 pi all over 60 radians per second. So, what is the speed? The speed is omega times R. In this case, we called our R L, so we'll plug that in and we've got omega which is 100 times 2 pi, divided by 60. L is 70 centimeters, which is 0.7 meters. Right we've got to keep this in SI units. And if somebody helps me with their calculator, let's see what we get for that. And I will approximate it here, 100 times .70 is 70. Two pi is about 6, a little bit more but that's all right. And so, we're going to get the 6's canceling out. We're going to get 70 over 10, which is about 7. And then 2 pi is actually a little bit bigger than 6, right? And so let's say this is maybe 7.2 meters per second. Anybody run it in a calculator? >> (student speaking) 7.33. >> 7.3? Okay so we were really close. 7.3 meters per second. That's how fast Brian Boitano's hands are moving as he spins in a circle. Which is you know roughly 15 miles per hour. Sounds reasonable, like pretty reasonable.

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