Question

A potter's wheel, with rotational inertia 24 kg*m^2 is spinning freely at 40 rpm The potter drops a lump of clay onto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay?

Answer 1

Concepts and reason

The concepts used to solve this problem are angular momentum, moment of inertia, and conservation of angular momentum.

First, use the relationship between the moment of inertia, angular velocity, and angular momentum to calculate the initial and final angular momenta of potter’s wheel.

Then, use the concept of conservation of angular momentum to calculate the mass of the clay.

Fundamentals

The tendency to resist the angular acceleration of a body is called as moment of inertia.

The expression for the moment of inertia of wheel is as follows:

Here, the moment of inertia is , mass is , and the perpendicular distance to the rotation axis is .

The expression for the angular momentum is as follows:

$L=10 $

Here, the angular momentum is and the angular velocity is .

The conservation of momentum states that the initial angular momentum is equal to the final angular momentum.

The expression for the conservation of momentum is as follows:

$1= $

Here, the initial angular momentum is and the final angular momentum is .

The expression for the initial angular momentum of potter’s wheel is as follows:

Substitute for and for .

After dropping the lump of the clay, the new moment of inertia of the system is as follows:

Here, the mass of the clay is and the perpendicular distance to the rotation axis of clay is .

Substitute for , and for .

The final angular momentum of potter’s wheel is as follows:

Substitute for and for .

The expression for the conservation of momentum is as follows:

$1= $

Substitute for and for .

Rearrange and calculate the value of .

Ans:

The mass of the clay is .