Question

a potter's wheel is a uniform disk of mass of 8.0 kg and radius 20.0 cm. a 3.0-kg lump of clay, roughly cylindrical with radius 4.0 cm, is placed at the center of the wheel. the wheel initially rotates at 40.0 rev/min. the clay then flattens into a disk of radius 12 cm. what is the final angular speed of the wheel?select answer from the options below44.7 rev/min35.8 rev/min42.3 rev/min40.0 rev/min37.8 rev/min

Answer 1

The final angular speed of the potter's wheel after the clay flattens into a disk is 0 rev/min.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of angular momentum, which states that the initial and final angular momentum of a system remains constant in the absence of external torques.

Initially, the potter's wheel is at rest, so its initial angular momentum is zero. When the clay is placed at the center of the wheel, it starts rotating with the wheel due to the conservation of angular momentum.

Let's assume the final angular speed of the wheel is ω. The final angular momentum of the system, considering the clay as a point mass, is given by:

Lf = (mwheel + mclay) * ω * rfinal + mclay * ω * 0,

where mwheel is the mass of the wheel, mclay is the mass of the clay, rfinal is the final radius of the clay, and 0 is the distance of the clay from its own center of mass.

Since the initial angular momentum is zero, we can equate it to the final angular momentum and solve for ω:

0 = (mwheel + mclay) * ω * rfinal + mclay * ω * 0,

From the equation, we can see that ω = 0, which means the final angular speed of the wheel is 0 rev/min. Therefore, the correct answer is 40.0 rev/min.