A potter's wheel (assuming a uniform disk of mass 5.0 kg and diameter 0.50 m) rotates around a vertical axis through its center at a frequency of 10 rad/s. The potter throws a 4.0-kg chunk of clay, shaped as a flat disk of radius 6.0 cm, onto the center of the rotating wheel. The frequency of rotation of the wheel after the clay sticks to it is
A) 8.4 rad/s.
B) 9.6 rad/s.
C) 10 rad/s.
D) 12 rad/s.
E) 19 rad/s.

Question

Quizplus · Accepted Answer

The conservation of angular momentum applies here. The initial angular momentum of the system is the angular momentum of the wheel alone, which is I_w * ω_i, where I_w is the moment of inertia of the wheel and ω_i is the initial angular velocity. The moment of inertia of the wheel is (1/2) * m_w * r_w^2. After the clay sticks, the total moment of inertia is I_w + I_c, where I_c is the moment of inertia of the clay, (1/2) * m_c * r_c^2. The final angular velocity ω_f is found using L_initial = L_final, or I_w * ω_i = (I_w + I_c) * ω_f. Solving for ω_f gives approximately 9.6 rad/s.

A Potter's Wheel (Assuming a Uniform Disk of Mass 5