This Charming Man of Science
Last week, fleurdusang introduced me to the song "This Charming Man" by The Smiths, followed by a brief discussion of flowers in back pockets. Being the nerd that I am, I got distracted by Morrissey swinging those flowers because it reminded me of all the angular momentum problems in my physics class last year.
I decided that it would be lulzy to re-write one of those problems to include Morrissey himself, instead of the random child swinging a ball on a string. Now that I'm home and found my physics textbook, I took the time to elaborate that idea into the post you see here.
This one's for you, Floor. ;D
Problem: The Smiths are preparing to film the music video for their song, "This Charming Man." In what seems to be a departure from his usual moroseness, the lead singer, Morrissey, decides to swing a cheery bunch of flowers in a circle over his head in a horizontal plane. He doesn't feel the need to swing them in tempo, but rather swings them moodily at a race of one revolution per 0.55 seconds. The flowers weigh 100 grams, and the stems are 0.45 meters long. What is the magnitude of the angular momentum of the flowers about the axis of Morrissey's hand?
Solution: Obviously I simplified the problem quite a bit - I treated the problem as a rigid rotor, where the stems are a mass-less rotor and the flowers are the particle at its end. Morrissey waffles around a little in terms of the frequency of the swings, so I focused in on 1:09 in the video, where he starts swinging them over his head, and yes, I did bust out my stopwatch to time that sucker.
Luckily, transforming the twirling to the model of the rigid rotor simplifies the problem immensely, and the system can then be described by the equation:
mag(L) = m(r^2)(w)
where mag(L) = magnitude of angular momentum (just the value, not the direction), r = radius of the circular path (here, the stem length), and w = angular frequency (technically this should be an omega, it's 2(pi) divided by the time of each revolution, aka the period).
The problem then becomes a plug-and-chug, where you substitute the numbers and get it done:
mag(L) = (0.1 kg) (0.45 m)^2 (2(pi)/0.55 sec)
mag(L) = 0.231 kg*m^2 / sec
Unfortunately those units don't simplify, so we have that ungainly number, but the magnitude is fairly small. That's to be expected, because the flowers don't weigh too much and he's not swinging them extremely fast. Now picture Morrissey gently batting people in the face with those flowers, and you'll be in the mindset that I was while I was writing this problem.
For comparison and citing purposes, the original random-child-swinging-a-ball problem was found in the textbook The Six Ideas That Shaped Physics, 2nd Edition, Unit C: Conservation Laws Constrain Interactions, as problem C13T.1.
I decided that it would be lulzy to re-write one of those problems to include Morrissey himself, instead of the random child swinging a ball on a string. Now that I'm home and found my physics textbook, I took the time to elaborate that idea into the post you see here.
This one's for you, Floor. ;D
Problem: The Smiths are preparing to film the music video for their song, "This Charming Man." In what seems to be a departure from his usual moroseness, the lead singer, Morrissey, decides to swing a cheery bunch of flowers in a circle over his head in a horizontal plane. He doesn't feel the need to swing them in tempo, but rather swings them moodily at a race of one revolution per 0.55 seconds. The flowers weigh 100 grams, and the stems are 0.45 meters long. What is the magnitude of the angular momentum of the flowers about the axis of Morrissey's hand?
Solution: Obviously I simplified the problem quite a bit - I treated the problem as a rigid rotor, where the stems are a mass-less rotor and the flowers are the particle at its end. Morrissey waffles around a little in terms of the frequency of the swings, so I focused in on 1:09 in the video, where he starts swinging them over his head, and yes, I did bust out my stopwatch to time that sucker.
Luckily, transforming the twirling to the model of the rigid rotor simplifies the problem immensely, and the system can then be described by the equation:
mag(L) = m(r^2)(w)
where mag(L) = magnitude of angular momentum (just the value, not the direction), r = radius of the circular path (here, the stem length), and w = angular frequency (technically this should be an omega, it's 2(pi) divided by the time of each revolution, aka the period).
The problem then becomes a plug-and-chug, where you substitute the numbers and get it done:
mag(L) = (0.1 kg) (0.45 m)^2 (2(pi)/0.55 sec)
mag(L) = 0.231 kg*m^2 / sec
Unfortunately those units don't simplify, so we have that ungainly number, but the magnitude is fairly small. That's to be expected, because the flowers don't weigh too much and he's not swinging them extremely fast. Now picture Morrissey gently batting people in the face with those flowers, and you'll be in the mindset that I was while I was writing this problem.
For comparison and citing purposes, the original random-child-swinging-a-ball problem was found in the textbook The Six Ideas That Shaped Physics, 2nd Edition, Unit C: Conservation Laws Constrain Interactions, as problem C13T.1.