A Glitch During Free Fall

Classical Mechanics Level 4

A uniform rod of mass $m$ and length $l$ is falling freely with it's center of mass moving with a velocity $v$ and both the ends horizontal, without any form of rotational motion. One of it's ends suddenly gets hinged and the rod starts rotating about that end.

If the angular speed with which the rod starts rotating is $k \left(\dfrac{v}{l}\right)$ , find $k$ .

Neglect air resistance and friction at the hinge also take $g=10\text{ m/s}^2$ .

2 3 It will not rotate 1 1.5

1 solution

Nihar Mahajan
Dec 30, 2016

Though there is torque of gravity, the duration of impact of hinging about one end is almost negligible hence, the angular momentum about that point is conserved. Using this fact,

$L=I\omega \implies mv\dfrac{l}{2}=\dfrac{ml^2}{3} \cdot \omega \implies \omega=\boxed{\dfrac{3v}{2l}}$

It would be great to add in you solution that the gravitational force (however has a torque about the hinged end) will not change angular momentum because the duration of impact is negligible.

R G Staff - 4 years, 5 months ago

A Glitch During Free Fall

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