A pendulum is hanging in a lift and is oscillating. The lift is given a free fall. What will happen to the bob of the pendulum?

Asked by: Sameer Modi

Answer

It depends on the time when free fall starts. The bob
will continue to move it's angular motion without any
change in its angular speed -so the angular momentum-
with respect to freely falling lift.

At this point (start of free falling) there is no gravity
force felt inside the lift. So you can imagine it like a
room in space where there is no gravity. Since there
is no gravity, there is no external force acting on
pendulum other then the force acting on its pin due to
circular motion (due to acceleration towards the origin),
but this force doesn't change the angular momentum w.r.t.
pin because it's acting on the pin where the radius is
zero.

So, we have two cases for the angular momentum just
before free falling; angular momentum is zero or not.

First Case: Just before free falling, the pendulum is at its
widest angle (highest point), where the angular velocity
is zero. It's at rest instantaneously. It continues to
stay at this position with respect to lift. (Until the
lift crashes when it hits to ground :-))

Second Case: Just before free falling, the angle of pendulum
is at some angle other then the maximum, where it has
some speed. It continues to rotate with this -constant-
angular speed while free falling until it hits the ceiling.
Answered by: Taylan Akdogan, Physics Ph.D. Candidate, M.I.T.

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