A small block on a frictionless, horizontal surface has a mass of 0.0250 kg. It is attached to a massless cord passing through a hole in the surface (Fig). The block is originally revolving at a distance of 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 the circle in which the block revolves to 0.150 m. Model the block as a particle. (a) Is the angular momentum of the block conserved? Why or why not? (b) What is the new angular speed? (c) Find the change in kinetic energy of the block. (d) How much work was done in pulling the cord? Figure:

Solution 42E Step 1 of 4: (a) Yes, angular momentum is conserved. The moment arm for the tension in the cord is zero so this force exerts no torque and there is no net torque on the block. Step 2 of 4: b)L = L so I = I 1 2 1 1 2 2 2 I = mr ( because block trated as a point mass) mr = mr 2 1 1 2 2 1 2 2 ( 1 2 = 1.75 rad /s( 0.3)2 0.15 = 7 rad/s