Using Integrals to Derive Rotational Inertia of a Long, Thin Rod with Demonstration

What is the integral used to calculate the rotational inertia of a rigid object?

• Integral of r with respect to time

• Integral of r cubed with respect to mass

• Integral of r squared with respect to mass

• Integral of mass with respect to r

How is the linear mass density (lambda) of a uniform rod defined?

• Length of a small piece divided by its mass

• Total length divided by total mass

• Mass of a small piece divided by its length

• Total mass divided by total length

What is the rotational inertia of a uniform rigid rod about one end?

• 1/12 times the mass times the length squared

• 1/3 times the mass times the length squared

• 1/2 times the mass times the length squared

• 1/4 times the mass times the length squared

In the practical example, how far is the inner end of the rod from the axis of rotation of the pulley?

• 0.305 meters

• 30.5 centimeters

• 3.05 meters

• 3.05 centimeters

What is the calculated rotational inertia of one spoke in the demonstrator?

• 0.443 times the mass times the length squared

• 0.233 times the mass times the length squared

• 0.331 times the mass times the length squared

• 0.133 times the mass times the length squared

What was the measured rotational inertia of the demonstrator with four spokes?

• 0.0119 kg·m²

• 0.0145 kg·m²

• 0.0137 kg·m²

• 0.0129 kg·m²

What was the relative error between the measured and predicted rotational inertia values?

• 6%

• 7%

• 4%

• 5%