Help! I\'m so confused.... A small blob of putty of mass m = 75.0 g falls from t

Question

Help! I'm so confused....

A small blob of putty of mass m = 75.0 g falls from the ceiling andlands on the outer rim of a turntable of radius R = 15.0 cm andmoment of inertia I = 1.70E-2 kg·m2 that isrotating freely with angular speed 3.77 rad/s about its verticalfixed-symmetry axis. What is the postcollision angular speed of theturntable-putty system? Thanks!
Help! I'm so confused....

A small blob of putty of mass m = 75.0 g falls from the ceiling andlands on the outer rim of a turntable of radius R = 15.0 cm andmoment of inertia I = 1.70E-2 kg·m2 that isrotating freely with angular speed 3.77 rad/s about its verticalfixed-symmetry axis. What is the postcollision angular speed of theturntable-putty system? Thanks!

Explanation / Answer

mass m = 75 g = 0.075 kg radius r = 15 cm = 0.15 m Initial moment of inertia I = 1.7 * 10 ^ -2 kg m ^2 initial angular speed w = 3.77 rad / s final moment of inertia I ' = I + mr^2                                       = 1.7 * 10 ^ -2 + 0.16875 * 10 ^ -2                                        =1.86875 * 10 ^ -2 kg m ^ 2 So, new angular speed w ' = Iw / I '                                         = 3.429 rad / s

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