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Re: The sign of g



I have found that one dimensional kinematics/dynamics is clarified for the
un-washed if every one dimensional vector is explicitly written as a
magnitude and a unit vector. One need only define, once and for all, the
positive direction of a single unit vector.

For vertical free fall, define [k] as the unit vector pointing vertically
up, once and for all. Then the free fall acceleration vector is
always -g[k], where g is the positive magnitude 32 ft/s^2 or 9.8 m/s^2.

Eg: the vertical free fall velocity vector is then given by:
v[k] = vo[k] -tg[k] . Stress that the numbers v and vo carry a sign, and
[k] always denotes the same (upward) direction.

After students are used to this formalism, they can "cancel" the unit
vector out of such one dimensional vector equations. I think it should be
stressed that this is only to ease writing pains; the direction is still
implicitly there - in each term. They are one-dimensional VECTOR
equations.

PS: All of the above could be done using the alternate definition of [k]
as vertically DOWN.
Then the free fall acceleration is always g[k], with g=32ft/s^2 . . . and
v[k] = vo[k] + tg[k]

In assigning/interpreting numerical values to/of v and vo, due account
must be taken of one's previous choice of definition for the unit vector
[k].

PPS: This pedagogy is why I always introduced the general 3D vector
concept BEFORE doing one-dimensional kinematics.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor


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