A thin, uniform bar of length L and mass M is suspended horizontally at rest. It...

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Physics

A thin, uniform bar of length L and mass M is suspendedhorizontally at rest. It is suddenly released
and, at the same instant, it is struck a sharp blow verticallyupwards at one end â€“ the duration of
the impulse is negligibly short.
(a) Explain the meaning of the equation Fnet = Macom (com standsfor center of mass). If we call z the vertical direction, write anequation for zCOM(t), draw a sketch of zCOM(t) vs t, and annotateit to show the initial
slope, the maximum value of zCOM(t), and the time(s) at whichzCOM(t) = 0.
(b) Explain the meaning of the equation Tnet = IÎ± (net torque).Describe the rotational motion of the bar, by
giving an equation for the angular displacement Î¸(t). (Themoment of inertia of a bar about
a perpendicular axis through its centre is 1/12ML^2.)
(c) By combining your answers to (a) and (b), describe in wordshow the bar moves after being
struck. (Note: you can try the experiment yourself, using a penas the bar, and your ï¬nger
or another pen to impart the impulse.)

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4.3 Ratings (639 Votes)

We are given a uniform bar of lengthand mass that is suspended horizontally When it is dropped suddenly alsogiving a struck at the same instant the bar falls down under theinfluence of gravity also rotating about the centre of massWe are dealing with a rigidextended object here So the usual Newtons law is not valid hereas it is applicable only for point particles However the samestructure of Newtons law can be reproduced for a system ofparticles based on the observation that for any system thattraverses along with the system as if it were a particle and itstrajectory as specified by Newtons law for point particles Such apoint is called the centre of mass com of the system Theconsequence is that the com of an object thus moves like a particlethat is acted upon by a force according to Newtons lawwhere is the total mass of the object and is the acceleration of the comThus once we knowthe com or the mass distribution of an object it is possible togive an account of the trajectory of the particle However youshould understand that this is not the actual trajectory of theparticle but the See Answer

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