A particle is moving in a circle of radius R with initial speed v It starts retarding with constant - Physics - Motion in a Plane

Question

A particle is moving in a circle of radius R with initial speed v
It starts retarding with constant retardation of v2 / 4πR The
number of revolutions it makes in time 8πR/v is ?

Sanjay Singh · Accepted Answer

Dear student
Distance moved by particle along circle before coming to restv2-u2=2as0-v2=-2asv2=2asv2=2ass=v22a=v2×4π×R2×v2=2πRangle moved=distance movedradiusθ=2πRR=2π which is equal to one revolutiontime taken by particle to stopv=u-at0=v-v2t4πRt=4πRvTime left for the particle to move 8πRv-4πRv=4πRvNow the particle stops for a moment and starts rotating in opposite directionDistance moved by particle along circle in time 4πRv starting from rests=ut+12at2=12at2=v24πR×(4πRv)22=2πRθ=2πRR=2π  which is equal to one revolution S0 total number of rotation is 2Regards

A particle is moving in a circle of radius R with initial speed v. It starts retarding with constant retardation of v2 / 4πR. The number of revolutions it makes in time 8πR/v is ?