A large wooden turntable in the shape of a flat uniform disk has a radius of 1.6

Question

A large wooden turntable in the shape of a flat uniform disk has a radius of 1.65 m and a total mass of 135 kg. The turntable is initially rotating at 3.10 rad/s about a vertical axis through its center. Suddenly, a 65.5-kg parachutist makes a soft landing on the turntable at a point near the outer edge.

(a) Find the angular speed of the turntable after the parachutist lands. (Assume that you can treat the parachutist as a particle.) 1.04 Incorrect: Your answer is incorrect. rad/s

(b) Compute the kinetic energy of the system before and after the parachutist lands. KEbefore = 883.1 Correct: Your answer is correct. J

KEafter = 297.3 Incorrect: Your answer is incorrect. J

Explanation / Answer

here,

mass of table , m1 = 135 kg

mass of Parachuist , m2 = 65.5 kg

initial speed , w0 = 3.1 rad/s

a)

let the final angular speed be w

using conservation of agular momentum

0.5 * m1 * r^2 * w0 = ( 0.5 * m1 * r^2 + m2 * r^2 ) * w

0.5 * 135 * 1.65^2 * 3.1 = ( 0.5 * 135 * 1.65^2 + 65.5 * 1.65^2) * w

solving for w

w = 1.57 rad/s

the final angular speed is 1.57 rad/s

b)

the initial kinetic energy , KE0 = 0.5 * I * w0^2

KEi = 0.5 * m1 * r^2 * w0^2

KEi = 0.5 * 0.5 * 135 * 1.65^2 * 3.1^2 J

KEi = 883.1 J

the final kinetic energy , KEf = 0.5 * (0.5 * m1 * r^2 + m2 * r^2 ) * w

KEf = 0.5 * ( 0.5 * 135 * 1.65^2 + 65.5 * 1.65^2) * 1.57 J

KEf = 284.2 J

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