IIT JEE , AIEEE Forum - Physics , Mechanics

iitjee08aspirant

a particle moves in a circle with a uniform speed when it goes from a point A to a diametrically opp point B the momentum of the particle changes by P_A-P_B=2kgm/s(j) and the centripetal force acting on it changes by F_A-F_B=8N(i) where i and j r unit vectors then angular velocity of the particle is
[ans:4 rad/sec]

rates assured............

iitjee08aspirant

3 days ................3 que............NO ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!
cumon plzzz answer atleast one of my questions...................
i posted 3 in last 3 days and only one has been answered ....
i dont think that i put question which arent worth of ur efforts????
is it so????

akhil_o

when they are at diametrically opp. positions velocity is in opposite directions

hence dP= mv-mu= mu-(-mu)=2mu

2mu=2

hnece mu=1 kgm/s

similarly

2mv²/r=8

mv²/r=4

(mv)v/r=1(4)

hence v/r=4

but v/r=ang velocity

hence

w=4

loyalgooner

Imagine the circle to have the center as the origin and it is rotating about the origin in anti clockwise direction. Now suppose initially the particle is at right most point,say if the circle has radius r then the point is at (r,0), now here the centripetal force would act along negative x direction. Now as it comes to point to diametrically opposite point at (-r,0) the force changes direction and is in +ve X direction although the magnitude remains same coz its uniform circular motion.

So suppose the magnitude is F, so initially the centripetal force is -F i cap and then it becomes +F i cap, so difference = 2F i cap = 8N i cap

Thus F = 4 N.

Similarly initially the momentum is say -p j cap (anti clw motion) and final is +p j cap. So difference is 2p j cap = 2 kg m/s and so p = 1 kgm/s.

Now F = mv^2/r=4 and p=mv=1

Thus putting value of m=1/v in F we get v/r = 4 But v/r = omega

So omega w = 4 rad/s.

iitjee08aspirant

THANKS A LOT DUDE!!!!!!!!!!!!!!!!!!!!!!!

anant_c

at A :momentum =mv(i)
at B:momentum =-mv(i)
therefore 2mv=2or mv=1.....(1)

F(A)=mv^2/r (j)
F(B) =-mv^2/r(j)

2mv^2/r=8...........(2)

and u have angular speed of the position vector = v/r.....(3)
Solve and get the answer

Ask & Discuss Questions with Community & Experts