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[Phys-L] real-world physics : sport : rotational + linear motion



Hi --

I've seen a lot of textbooks that don't do nearly enough to
connect physics principles to real-world applications. A good
teacher can make up for this by "enriching" the discussion with
real-world examples, but it takes a lot of effort to come up with
suitable examples.

Students often find it particularly hard to see any connection
between the real world and the physics of rotational motion.
However, _sports_ provide several entire categories of interesting
applications, especially if we are willing to consider the
/combination/ of linear motion with rotational motion.

1) A particularly simple yet interesting question is this: on a
billiard table, how high should the cushion be? The numerical
answer is surprisingly simple:
http://plus.maths.org/content/outer-space-cushioning-blow

If students have access to a pool table they can experiment with,
it takes only a few seconds to demonstrate that a bouncing off a
properly-designed cushion (0.7D) is far, far better than bouncing
off (say) a blank wall (effectively 0.5D). With a small amount
of preparation, you can set up a classroom demo of this; you don't
need a full pool table. Scaling up to a basketball makes the
details easier to see. Also note that there are several different
"standard" sizes of pool balls in the world. I once saw some games
played with balls that were mismatched to the height of the cushion.
It was quite weird. Sometimes it pays to get the physics right.

2) The physics of a golf swing is interesting. The key idea is
that you (primarily) do not manipulate the golf club with your
wrists the way a drummer manipulates drumsticks. Instead you
(primarily) use your arms and upper body to move the handle.
Because the handle is far from the center of mass, this imparts
a rotational motion. The full analysis is too complicated for
the introductory class, but you can do a simplified version,
using the impulse approximation: Take an initially stationary
club and impart a sideways impulse to the end of the handle.
Explain what happens next. You can simulate this and draw nice
graphics using nothing more than a spreadsheet.

I'm not an expert, but as I understand it, for a proper golf swing
most of the motion (including the rotation) is confined to a single
two-dimensional plane.

3) The physics of swinging a baseball bat is similar, only more
complicated, because the motion is fully three-dimensional. Even
if you approximate the knob of the bat as moving in the XY plane,
the bat is initially sticking up in the Z direction, so the full
motion is very complicated. However, the point remains that the
physics principles involved are quite simple. In particular, there
is a combination of linear and rotational motion. The fact that
you grip the bat far from its center of mass allows you to impart
a tremendous amount of rotational energy to it, far more than you
could using wrist-strength alone.

The full biomechanics of a baseball swing is a topic of current
research. I mention this because it means students can see at
least the outline of a connection between what they are studying
and 100% practical 100% state-of-the art physics.

References:
2D:
http://www.physics.usyd.edu.au/~cross/baseball.html
3D:
http://scholarlyrepository.miami.edu/cgi/viewcontent.cgi?article=1550&context=oa_dissertations
http://www.swingstabilizer.com/assets/hitting_mechanics.pdf
http://www.springerlink.com/content/b86k070853011305/