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21. Problem 12.39 (HR) A meter stick is held vertically with one end on the floor and is then allowed to fall. We have to find the speed of the other end when it hits the floor, assuming that the end on the floor does not slip. |
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Solution: Click For PDF Version The moment of inertia of a stick of length l and mass m about
an axis passing through one of its end is
or
The speed of the end of the stick of length l when it touches the ground on falling with one of its ends remaining fixed will be
As,
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. The
centre of gravity of a stick of length l standing vertically will be at a
height
from its
base. Therefore, the potential energy of the stick standing vertically will be
. Let the
angular speed of the top end of the stick when it hits the ground be
.
By applying the principle of conservation of energy we can obtain an equation
that gives the angular speed of the stick as it hits the ground. It is
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