Question Video: Calculating the Angular Momentum of an Iron Weight in Circular Motion

A 2.0 kg cast iron weight is swung around in a circle at 1.5 m/s at the end of a rope. The rope has a length of 1.2 m. What is the magnitude of the angular momentum of the iron weight?

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Video Transcript

A 2.0-kilogram cast iron weight is swung around in a circle at 1.5 meters per second at the end of a rope. The rope has a length of 1.2 meters. What is the magnitude of the angular momentum of the iron weight?

Since this is a mechanics problem about a weight moving in a circle, let’s draw a picture to organize our information. Here is our label diagram. We have the cast iron weight labeled with its mass of 2.0 kilograms. We’ve also labeled the speed of the cast iron weight as 1.5 meters per second. We’ve arbitrarily chosen to draw the direction of motion as clockwise because we aren’t told the direction in the question. And anyways, we only want the magnitude of the angular momentum. Finally, we also have the rope labeled with its length of 1.2 meters. Notice that the rope forms the radius of the circular path traced out by the weight. We’ve also written a label for the unknown size of the angular momentum since that’s what we’re looking for.

Let’s now recall the formula for the angular momentum of an object moving in a circle. We have for the angular momentum of an object moving in a circle that the size of the angular momentum is equal to the radius of the circle times the mass of the object times the tangential speed of the object. Recognizing that mass times tangential speed is the same as the linear momentum of the object, we can see that this formula also agrees with the definition of angular momentum as the radius of the circle times the linear momentum of the object. Remember, this formula gives the angular momentum about the center of a circle. Since our question didn’t explicitly state otherwise, we can assume that the angular momentum that it’s looking for is referenced to the center of the circle.

Since we already have the mass of the object, its tangential speed, and also the radius of the circle, all we need to do is plug in values. We have that the angular momentum that we’re looking for is 1.2 meters times 2.0 kilograms times 1.5 meters per second. Collecting the numbers first, 1.2 times 2.0 times 1.5 is exactly 3.6. And now collecting units, meters times kilograms times meters per second is kilograms meters squared per second, which is the units of angular momentum. So the magnitude of the angular momentum of the cast iron weight is 3.6 kilograms meters squared per second. This is the magnitude of the angular momentum about the center of the circle since that’s the assumed reference point for our problem.

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