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.
