Determine the final velocities for the two pucks. Calculate the initial and fina

Question

Determine the final velocities for the two pucks. Calculate the initial and final translational kinetic energy for the system. If the diameters of each of the pucks is 6cm . calculate the fn.il angular velocity for each, assuming there is no initial rotation of the incoming puck. A uniform solid disk with a mass of 2.0 kg and 20 cm m diameter rotating about an axis through Its center at 200 rpm A circular hoop. 20 0 cm m diameter with a mass of 1 0 kg. Is dropped straight down onto the rotating disk. Friction between the disk and hoop causes the hoop to accelerate until it rotates with the disk at rest with respect to the disk. Calculate the final angular velocity of the combination.

Explanation / Answer

here,

mass of the disk , md = 2 kg

mass of the hoop , mh = 1 kg

radius of the hoop , rh = 0.1 m

radius of the disk , rd = 0.1 m

initial speed of thedisk , w = 200 rpm

w = 20.93 rad/s

let the final angular speed be w'

using conservation of angular momentum about the central axis

Id*w = ( Id + Ih)*w'

0.5 * 2 * 0.1^2*20.93 = ( 0.5 * 2 * 0.1^2 + 1*0.1^2) * w'

w' = 10.47 rad/s

the final angular speed of the combination is 10.47 rad/s

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