A particular horizontal turntable can be modeled as a uniform disk with a mass o

Question

A particular horizontal turntable can be modeled as a uniform disk with a mass of 180 g and a radius of 24.0 cm that rotates without friction about a vertical axis passing through its center. The angular speed of the turntable is 6.00 rad/s. A ball of clay, with a mass of 40.0 g, is dropped from a height of 35.0 cm above the turntable. It hits the turntable at a distance of 15.0 cm from the middle, and sticks where it hits. Assuming the turntable is firmly supported by its axle so it remains horizontal at all times, find the final angular speed of the turntable-clay system.

the answer 5.52 isn't correct. please explain your process don't just put the work down or else the answer isn't really helpful for learning just helpful for my grade. thanks!!

Explanation / Answer

Here,

m1 = 180 gm = 0.180 Kg

radius ,r = 24 cm = 0.24 m

angular speed , wi = 6 rad/s

mass of clay , m2 = 0.040 gm

d = 15 cm = 0.15 m

Using conservation of angular momentum

(m1 * r^2 * 0.5 ) * wi = (0.5 * m1 * r^2 + m2 * d^2 ) * w2

(0.18 * 0.24^2 * 0.5 ) * 6 = (0.5 * 0.180 * 0.24^2 + 0.040 * 0.15^2) * w2

solving for w2

w2 = 5.11 rad/s

the final angular speed of the system is 5.11 rad/s

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