A physics problem related with rotation.?

Question

A cockroach of mass m lies on the rim of a uniform disk of mass 2.32m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.261 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? (b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?

Answer 1

The system will obey conservation of momentum

Ii*wi=Io*wo

Ii=.5*2.32*m*R^2+m*R^2
=m*R^2*3.32
and wi=0.261

Io=.5*2.32*m*R^2+m*R^2/4
=m*R^2*2.57

so
wo=3.32*0.261/2.57
0.337 rad/s

Kinetic energy is
.5*I*w^2

I will solve for Ko/Ki
(2.57*0.337^2)/(3.32*0.261^2)
=1.29
The increase in energy came from the work done by the cockroach to move inward.

j

Answer 2

r' = r*cos(L) v = r'*2*pi/seconds_in(24hours) a = v^2/r' Now in case you do use this Accel to characteristic to gravity, remember they're vectors and by no skill inevitably performing interior an analogous route. Is that adequate to get you all started (i do not pick to ruin all of your thrilling)