Question

The answer is -66.7% please show me how to get to this answer. Please be detailed and show step by step.

5. As shown on the right, a uniform disk with M = 1.000 kg and D = 50.00 cm is initially rotating at 10.00 radians/s when a non-rotating thin ring of the same mass and radius is gently dropped vertically onto it. Their centers of mass and axes of rotation align after the perfectly inelastic collision. What percentage of the initial rotational kinetic energy of the disk is converted to heat and sound during the collision? Given: 1t -MR, Idisk-1/2 MR2 thin ring Hint: Save time, work out all the algebra, and simplify your final equation, before substituting in the values! % KErot converted?-66.7 %

Answer 1

here,

mass , m = 1 kg

radius , r = D/2 = 0.25 m

initial angular speed , w0 = 10 rad/s

let the final angular speed be w

using conservation of angular momentum

I * w = I0 * w0

(0.5 * m * r^2 + m * r^2) * w = (0.5 * m * r^2) * w0

1.5 * w = 0.5 * 10

w = 10 /3 rad/s

the percentage of initial kinetic energy converted lost , % = ( 0.5 * I0 * w0^2 - 0.5 * I * w^2) /( 0.5 * I0 * w0^2) * 100

% = ( 0.5 * m * r^2 * 10^2 - 1.5 * m * r^2 * (10/3)^2) /( 0.5 * m * r^2 * 10^2) * 100

% = 2/3 * 100 = 66.7 %