A small block on a frictionless horizontal surface has a mass of 2.50
m = 2.5*10^-2 kg
Initial radius of circualar motion, R = 0.27 m
Initial angular speed, Wi = 2 rad/s
final radius of circle, r = 0.2 m
Let Angular speed of mass after radius is reduced to 0.2, = Wf
Initial angular momentum, Mi = (m*R^2)*Wi
Final engular momentum, Mf = (m*r^2)*Wf
Now, by conservation of angular momentum,
Mi = Mf
a) Yes angular momentum is conserved
So, (m*R^2)*Wi = (m*r^2)*Wf
So, Wf = (R^2/r^2)*Wi = (0.27^2/0.2^2)*2 = 3.65 rad/s <------------answer(new angular speed)
c)
Change in Kinetic energy = 0.5*(mr^2)*Wf^2 - 0.5*(mR^2)*Wi^2
= 0.5*2.5*10^-2*((3.65*0.2)^2 - (2*0.27)^2) = 3.02*10^-3 J <-------answer
d)
Work done in pulling the cord = 3.02*10^-3 J <------- same as change in Kineitc energy
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