Question

A uniform disk A of mass m_A= 8.2 kg turns at ω_A=+50 rad/s about a fixed central axis. Another rotating disk B of mass m_B= 10.5 kg, with the same radius R of disk A, is dropped onto the freely spinning disk A (see figure). They become coupled and turn together with their centers superposed, as shown in the figure, with an angular velocity ω'=+33 rad/s. (The moment of inertia of the disk is  I_d = [ 1/2]mR², where m is the mass, and R is the radius) . The angular velocity of disk B before the impact is:

Answer 1

here,

mass of disk A , mA = 8.2 kg

mass of disk B , mB = 10.5 kg

initial angular speed of A , wA = 50 rad/s

radius of disks is R

the final angular speed , w' = 33 rad/s

let the angular velocity of the disk B before the impact be wB

using conservation of angular momentum

(0.5 * mA * R^2) * wA + (0.5 * mB * R^2) * wB = (0.5 * ( mA + mB) * R^2) * w'

(8.2 ) * 50 + (10.5 ) * wB = (( 8.2 + 10.5) ) * 33

solving for wB

wB = 19.7 rad/s

the angular velocity of the disk B before the impact is 19.7 rad/s