A thin horizontal uniform rod `AB` of mass `m` and length `l` can rotate freely about a vertical axis passing through its end `A`. At a certain moment, the end `B` starts experiencing a constant force `F` which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. The angular velocity of the rod as a function of its rotation angle `theta` measured relative to the initial position should be.
Text Solution
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Work done by the torque `/_\W=int taudtheta=int_(0)^(theta)Flcosthetad theta` `/_\W=Flsintheta` Now using work energy theorem `/_\W=/_\k` `:.Flsintheta=[1/2((ml^(2))/3)omega^(2)-0]` Which gives `omega=(sqrt(6Fsintheta)/(ml))`
A thin horizontal uniform rod AB of mass m and length l can rotate freely about a vertical axis passing through its end A . At a certain moment, the end B starts experiencing constant force F which is always perpendicular to the original position of the stationary rod and directed in a horizontal plane. Find the angular velocity of the rod as a function of its rotation angle phi counted relative to the initial position.
A thin horizontal uniform rod AB of mass m and length l can rotate freely about a vertical axis passing through its end A. At a certain moment the end B starts experiencing a constant force F which is always perpendicular to the original position of the stationary rod and directed in a horizonatal plane. Find the angular velocity of the rod as a function of its rotation angle varphi counted relative to the initial position.
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