Question
A small block on a frictionless horizontal surface has a mass of0.0250 kg. It is attached to a mass-less cord passing through ahole in the surface. The block is originally revolving at adistance 0.300 m from the hole with an angular speed of 1.75 rad/s.The cord is then pulled from below, shortening the radius of thecircle in which the block revolves to 0.150 m. You may treat theblock as a particle. (a) Is angular momentum conserved? Why or Whynot? (b) What is the new angular speed? (c) Find the change inkinetic energy of the block. (d) How much work was done in pullingthe cord?
Explanation / Answer
(a)Yes, total of a rotating object remains constant ifthe net external torque acting on it is 0. (b) I11=I22
mR1^21=mR2^22 2=1((R1^2)/(R2^2)) v=R v2=R22=R21((R1^2)/(R2^2))=v1(R1/R2)=1.75m/s(.3m/.15m)=3.5m/s (c)KE remains constant if remains constant (d) work =Force*distance force =1/2(v1^2+v2^2)/1/2(R1+R2) =7.66/.225 = 34 distance = .15 so work done = 5.1Nm