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A ring of mass m and radius r is lying on a horizontal table . A bullet of mass m moving with vel v strikses the ring tangentially and gets embedded in it . Find the vel of the bullet in the groungd frame just after the impact..SOLVE IT USING IMPULSE METHOD
Comments (13)
any free system has a tendency to rotate about its COM
COM of the system= midpoint of the radius joining the centre of the ring to the attached mass
now, linear impulse= J change in linear momentum
J=m(vc-v )=-mv/2
vc=v/2 by conservation of linear momentum,
angular impulse= change in angular momentum about COM
J=-mvr/4=Iw-mvr/2
mr2w/4=mvr/4
w=v/r
therefore, net velocity= v/2 +(r/2)w= v???
NO, you can conserve angular momentum about any point. See, before collision com of system is moving in straight line. By conservation of linear momentum com will continue along that line. As there is rotational motion after the collision this rotation will obviously take place about com of system as it moves along line. As rotation is about com of system conserving angular momentum about com becomes easier. When you conserve angular momentum about say, an axis placed initially at the centre of ring, then the final angular momentum will be written as L = Lc + mr/2v. Remember that the system is rotating about com of system C. About a stationary axis initially placed at ring centre the motion of the system is rotation + translation. the ring +particle system rotates about C. And therefore, the angular momentum of the system about a stationary axis initially placed at the centre of ring will be Lc + mr/2v. Where Lc is angular momentum of system about C(
Ic is MI of system about C). and v is velocity of C
L = Lc + m r /2X v
IF YOU CONSERVE ANGULAR MOMENTUM ABOUT C ITSELF THEN YOU DONT HAVE TO WORRY ABOUT MRV PART.
rates please..
if not understood nudge me
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let impulse imparted by point mass to the ring be J. Let final velocity of com of ring is v1 and final velocity of point mass is v2. angular velocity of ring be w. Then J = mv1, -J = mv2 - mv , and v2 = v1 + rw, and Jr = Iw
kindly rate if correct...