(2 of 2) Measuring the Rotational Inertia of a Bike Wheel

Summary

In this engaging physics class, Mr. P and his students explore the concept of rotational inertia by analyzing a bicycle wheel. They work through the process of measuring torques, calculating the force of tension, and understanding the relationship between mass, radius, and rotational inertia. The students ask insightful questions about the forces involved and the methods used to determine the wheel's rotational inertia. After a hands-on experiment with a force sensor, the class confirms their theoretical predictions, demonstrating the practical application of physics concepts. Through collaboration and problem-solving, they deepen their understanding of rotational motion and its real-world implications.

Takeaways

• 😀 The bicycle wheel's rotational inertia was measured as 0.147 kg·m², but its reasonableness needed verification.
• 😀 To check the rotational inertia, the equation for rotational inertia of objects like spheres and cylinders was applied, providing a reasonable estimate for the wheel.
• 😀 The rotational inertia of the bicycle wheel is calculated to be 0.680 times its mass and radius squared, which is within a reasonable range compared to a solid disk or thin hoop.
• 😀 The group discussed whether summing torques acting on both the wheel and the hanging mass would simplify the problem, but this approach isn't valid due to the complexities of defining the rotational inertia of the hanging mass.
• 😀 Bo questioned why only the wheel's torques were summed, leading to a discussion on defining the rotational inertia of the hanging mass around the wheel's axis of rotation.
• 😀 Bobby raised the idea of using the force of gravity instead of the force of tension in calculations, but this led to a deeper exploration of why tension needs to be calculated directly.
• 😀 The force of tension in the string during angular acceleration was calculated both from the torques acting on the wheel and the forces on the hanging mass, with both methods yielding consistent results.
• 😀 Before the wheel starts to accelerate, the tension in the string matches the gravitational force on the hanging mass (about 2.01 N).
• 😀 During acceleration, the force of tension in the string decreases, matching predictions with an observed differential of 0.3 N.
• 😀 The experimental results were considered close enough to the predictions, with a force differential of 0.3 N matching the theoretical value, leading to a conclusion that the physics is accurate.

Q & A

What is rotational inertia, and why is it important in this experiment?

Rotational inertia (or moment of inertia) is a measure of an object's resistance to changes in its rotational motion. It is important in this experiment because it determines how much torque is needed to rotate the bicycle wheel, and helps explain how the forces acting on the wheel (like tension and gravity) influence its angular acceleration.

How did the class measure the rotational inertia of the bicycle wheel?

The class used the net torque equation to solve for the rotational inertia of the wheel. They summed the torques acting on the wheel and used the measured radius, mass, and angular acceleration to compute the rotational inertia.

Why did the students use a fraction to estimate the rotational inertia of the bicycle wheel?

The students used a fraction to estimate the rotational inertia because the bicycle wheel is not exactly a thin hoop or a solid disk. Its inertia is somewhere between that of a hoop and a disk, so the fraction (between 0.5 and 1) represents this range.

What was the estimated rotational inertia of the bicycle wheel, and how was it verified?

The estimated rotational inertia of the bicycle wheel was 0.147 kg·m². This was verified by calculating the fraction of the wheel's mass and radius squared, yielding a result close to 0.680, which was within the expected range for a wheel of its type.

Why did Bo suggest summing the torques acting on both the wheel and the hanging mass?

Bo suggested summing the torques acting on both the wheel and the hanging mass to simplify the calculation, thinking the two torques caused by tension would cancel each other out. However, Mr. P explained that this approach is not valid without considering the complexities of defining the axis of rotation and calculating the torque for both objects separately.

What was Mr. P’s response to Bo’s suggestion of canceling the torques?

Mr. P explained that summing the torques on both the wheel and the hanging mass at the same time is not appropriate. The rotational inertia in the equation applies only to the wheel, and canceling out the torques caused by tension would not be valid since the torque vector for the hanging mass has not been defined.

What was the equation used to solve for the force of tension in the string?

The equation used to solve for the force of tension was derived from the torque equation for the wheel. It was rearranged to: Force of tension = (Rotational inertia × Angular acceleration) / Radius.

How did the students verify the force of tension experimentally?

The students used a wireless force sensor to measure the tension in the string. The sensor provided real-time measurements of the force of tension before the wheel was released and while it was accelerating, confirming the theoretical calculations with experimental data.

What was the force of tension measured before the wheel was released?

Before the wheel was released, the force of tension measured by the sensor was approximately 1.9 newtons.

What was the discrepancy between the predicted and measured values for the force of tension while the wheel was accelerating?

The predicted value for the force of tension while the wheel was accelerating was 1.7 newtons, while the measured value was 1.6 newtons. The difference of 0.1 newtons was considered acceptable, as it was a minor discrepancy.