[email hidden] writes:
The time it takes for the rod to topple is indeterminate. Imagine
that it were precisely balanced on its end---the duration would be
infinite. So timing the toppling is useless. The relevant measure
is the velocity at impact. In this case, the velocity at the tip
at impact. That is readily computed from conservation of energy.
Assume a uniform rod of length l, mass m. When standing on its end,
its potential energy is m*g*l/2. Assume that as it topples, its bottom
end does not slide (that is, acts as a pivot). When the tip strikes
the ground, all the potential energy has been converted to kinetic
energy. So
m*g*l/2 = 1/2*I*w^2
where
I = moment of inertia of rod, about one end = m*l^2/3
w = angular velocity of rod at impact
The velocity at the tip is
Vtip = w*l
so
Vtip = sqrt(3*g*l).
The same rod held horizontally and dropped from a height of l
has an impact velocity of
V = sqrt(2*g*l).
To achieve the same velocity as the toppling rod,
the horizontal rod must start at a height of 3/2*l.
Joe