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A thin uniform rod of length l is initia...

A thin uniform rod of length `l` is initially at rest with respect to an inertial frame of reference. The rod is tapped at one end perpendicular to its length. How far the centre of mass translates while the rod completes one revolution about its centre of mass. Neglect gravitational effect.

Text Solution

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Let `/_\t` be the duration of impact, then
`J=/_\vecP`
or `J=(Mv_(c)-0)` ….i

Angular impulse is equal to change in angular momentum
or `(Jl)/2=(/_\omega)`
`=I(omega-0)=(ml^(2))/12 omega`……..ii
Dividing eqn in by eqn ii we get
`omega=(6v_(0))/l`
Let t be the time inwhich the rod rotates at angle `2pi` then
`omegat=2piimpliest=(piL)/(3v_(0))`
Hence distance travelled by centre of mass `implies x_(c)=(lpi)/3`
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