# Waterwheel Torque and Rotational Inertia Calculation

How is torque exerted by a waterwheel calculated and how can it be used to find the rotational inertia of an object?

## Calculating Torque Exerted by Waterwheel

**Torque** is calculated by multiplying the force exerted by the water on the wheel by the radius of the wheel. The force can be determined using Newton's second law of motion, F = ma, where m is the mass of water flowing per second and a is the acceleration of the wheel. The torque can then be calculated by multiplying the force by the radius of the wheel.

## Finding Rotational Inertia of an Object

**Rotational inertia** of an object can be found using the equation I = torque / α, where I is the rotational inertia, torque is the torque exerted on the object, and α is the angular acceleration. By using the calculated torque and the given angular acceleration, the rotational inertia of the object can be determined.

Waterwheels are mechanisms used to convert kinetic energy into mechanical energy. In this scenario, if 10 kg of water flows onto a waterwheel with a radius of 3 m every second, the torque exerted by the waterwheel is 18 Nm. This torque causes the wheel to accelerate angularly at 0.6 rad/s². By using the calculated torque and the angular acceleration, we can find the object's rotational inertia.

The torque exerted by the waterwheel is calculated as follows:

Force (F) = Mass (m) * Acceleration (a) = 10 kg/s * 0.6 rad/s² = 6 N

Torque = Force (F) * Radius (r) = 6 N * 3 m = 18 Nm

To find the object's rotational inertia, we use the formula:

Rotational Inertia (I) = Torque / Angular Acceleration (α) = 18 Nm / 0.6 rad/s² = 30 kg·m²

This means that the rotational inertia of the object affected by the waterwheel's torque is 30 kg·m².