posted by darrin .
If a hollow metal cylinder of radius r is rolling towards a circular bump of height h.
calculate the minimum speed needed to progress over a circular bump.
at the top of the bump it stops rolling and stops going forward (teeters motionless)
Thus at the top the kinetic energy is zero and the potential energy is m g (r+h)
At the bottom the potential energy is m g r
so it gained potential energy of m g h
That is how much kinetic energy it lost
Ke = .5 m v^2 + .5 I w^2
I = m r^2
w = v/r
so in terms of v
Ke = .5 m v^2 + .5 m r^2 (v^2/r^2)
Ke = m v^2 total (half translational and half rotational)
m v^2 = m g h
v = sqrt (g h)