Final answer:
When the clay chunk is thrown onto the rotating potter's wheel, it sticks to it and causes the wheel to rotate at a slower rate. The final frequency of the wheel can be found using the principle of conservation of angular momentum.
Step-by-step explanation:
The frequency of a rotating object is the number of complete revolutions it makes per second.
In this problem, the original frequency of the potter's wheel is given as 2.0 rev/s.
When the clay chunk is thrown onto the wheel, it sticks to it, causing the wheel to have a larger moment of inertia and, consequently, rotate at a slower rate.
To find the final frequency, we can use the principle of conservation of angular momentum. The initial angular momentum of the potter's wheel is equal to the final angular momentum after the clay sticks to it.
The initial angular momentum of the potter's wheel can be calculated using the formula:
Li = Iiωi
where Li is the initial angular momentum, Ii is the initial moment of inertia, and ωi is the initial angular velocity.
Since the wheel is a uniform disk, its moment of inertia can be calculated using the formula:
Ii = 1/2 * m * ri2
where m is the mass of the wheel and ri is the radius of the wheel.
The final angular momentum of the combined system can be calculated as:
Lf = (Ii + Ic) * ωf
where Lf is the final angular momentum, Ic is the moment of inertia of the clay, and ωf is the final angular velocity.
Since the clay is approximately shaped as a flat disk, its moment of inertia can be calculated using the formula:
Ic = 1/2 * mc * rc2
where mc is the mass of the clay and rc is the radius of the clay.
Since angular momentum is conserved, we can equate the initial and final angular momenta:
Li = Lf
Substituting the expressions for angular momentum and moment of inertia, we have:
Ii * ωi = (Ii + Ic) * ωf
Now we can solve for ωf to find the final angular velocity of the wheel.