# Angular Momentum in the real world

Let's look at some examples of angular momentum in the real world.

When quarterbacks throw the football, they impart a spin with their fingers, so that the ball spins rapidly as it flies through the air. Football fans call a good pass a tight spiral.

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Q:  Why put spin on the ball?

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Screenshot from a DVD copy of GoldenEye. Image copyright for the film is owned by the Danjaq, L.L.C. & United Artists Pictures.

The pretty spiral pattern around the muzzle's exit hole are grooves cut into the barrel of a gun. Here's another example, from a 75mm artillery piece used by the French in World War 1.

Bullets which come out of a rifled barrel have grooves cut into them, like this one:

Image courtesy of Stretcher Bullet Pictures

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Q:  Why put spin on a bullet?

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Photo of Smith and Wesson handguns Copyright © by Jeff Dean. Photo of ammunition (JSP on left) courtesy of ReconTonto and Wikipedia Commons

Let's look at one particular example: a .357 Magnum revolver firing a Winchester 158 grain JSP bullet. We'll make a few approximations: that the bullet moves at its final speed throughout the muzzle, and that it follows the rifling grooves perfectly without slipping.

• bullet leaves muzzle with speed v = 1235 fps
• muzzle is rifled so that each twist requires d = 8.25 inches inside the barrel
• bullet is a solid cylinder of length L = 1.29 inches, diameter D = 0.357 inches (hence the name of the gun), and mass m = 158 grains = 10.2 grams
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Q:  What is the moment of inertia of the bullet around
its long axis?

Q:  What is the angular velocity of the bullet around
its long axis when it leaves the muzzle?

Q:  What is the angular momentum of the bullet around its
long axis in flight?

Q:  What fraction of the total kinetic energy of the bullet
is rotational KE?

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The Hubble Space Telescope floats freely in space.

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Q: How can astronomers change its orientation
so that it points to some particular star?

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Propellent might leave residue on the mirrors -- very bad. It would also be imprecise, since HST needs to make small movements accurate to about 0.1 arcseconds.

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Q: If there are 60 arcminutes in one degree,
and 60 arcseconds in one arcminute,
what is the angular precision required

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The answer: use reaction wheels, which are simply pairs of disks mounted inside the telescope structure.

Each reaction wheel is about 40 cm in diameter and has a mass of about 40 kg. They are used in pairs.

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HST may be approximated as a cylinder with

length   L = 13.3 m
diameter D = 4.3 m
mass     M = 11,110 kg

At full speed, it can slew in angle at about
the same speed as the minute hand on a clock.

Q:  How fast must the reaction wheels be
able to spin to cause this motion?