Answer:
1.56 rad/s
Explanation:
[tex]\omega_1[/tex] = 16 revolution/minute = 16 * 2π (rad/rev) * (1/60) (min/sec) = 1.68 rad/s
46 cm = 0.46 m
Treating the lump of clay as a point mass 46 cm from the rotational axis, the new rotational inertia of the system would be
[tex]I_2 = I_1 + mr^2 = 7.5 + 2.65*0.46^2 = 8.06 kgm^2[/tex]
According the the law of momentum conservation, the product of rotational inertia and angular speed must stay the same:
[tex]I_1\omega_1 = I_2\omega_2[/tex]
[tex]\omega_2 = \omega_1\frac{I_1}{I_2} = 1.68 * \frac{7.5}{8.06} = 1.56 rad/s[/tex]
