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A uniform rod of mass m and length is ac...

A uniform rod of mass `m` and length is acted upon by the forces `F_(1)` and `F_(2)` Find that:
a. linear-and angular acceleration of the rod.
b. value of `x` for which the point `P` does not accelerate.

Text Solution

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a. Equation of motion
`F_(1)+F_(2)=ma`
or `2F-F=maimpliesa=(3F)/m`…….i
torque equation about centre of mass.
`2F.l/2-F.x=((ml^(2))/12)alpha`
`implies alpha(12F(l-x))/(ml^(2))` ………ii
b. If point `P` does not acceleration
`veca_(P)=veca_(P,C)+veca_(C)`
As `a_(P)=0=-ax+aimpliesax=a`
`(12F(l-x))/(ml^(2))=(3F)/m`
which given `x=l/2`
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