Rotational Motion Homework: Angular Momentum and Tension

[bfr]

Homework Statement

I did a lab today where a weight was tied to a string. The string was wrapped around part of the circumference of a wheel, and then the end was taped down. So, when I let go of the wheel and the weight, the force of gravity on the weight causes the wheel to turn. I have two questions:

1. Is the angular momentum of the system made up of the wheel and the mass conserved?
2, Is the tension in the string constant?

Homework Equations

|Torque|=|F||r|sin(θ)
Angular momentum=I*$$\omega$$

The Attempt at a Solution

1. I think it isn't conserved because the force of gravity acting on the mass accelerates the system, making angular momentum not be conserved.
2. The tension is constant because it equals the mass of the weight times 9.8.

 

[Dr.D]

You say "the end was taped down." Do you mean the end of the string was taped down? If so, how did this permit the system to move?

With regard to the tension in the string, draw some FBDs and write some equations of motion before you jump to a conclusion here.

 

[nlightner]

I would like to clarify and expand upon the answers provided. First, it is important to understand the concept of angular momentum. Angular momentum is a measure of the rotational motion of an object and is defined as the product of its moment of inertia and angular velocity. In simpler terms, it is the measure of how much an object is rotating and how fast it is rotating.

Now, to answer the first question, the angular momentum of the system made up of the wheel and the mass is conserved. This means that the total angular momentum before and after the weight is released remains the same. This can be explained by the law of conservation of angular momentum, which states that in the absence of external torque, the angular momentum of a system remains constant. In this case, the only external torque acting on the system is due to the force of gravity on the weight. However, this torque is balanced by the torque produced by the tension in the string, which we will discuss in the next question.

Moving on to the second question, the tension in the string is not constant. As the weight falls, the tension in the string decreases due to the decrease in the radius of the wheel. This can be seen in the equation provided, where the torque is directly proportional to the radius. As the radius decreases, the torque decreases, and hence the tension decreases. However, as mentioned earlier, the torque due to gravity is balanced by the torque produced by the tension in the string. This means that the tension in the string is always equal to the force of gravity acting on the weight, which is equal to its mass multiplied by the gravitational acceleration (9.8 m/s^2).

In conclusion, the angular momentum of the system is conserved, while the tension in the string is not constant but is equal to the force of gravity acting on the weight. It is important to note that these answers are based on the assumptions that the string and the wheel are massless, and there is no friction between the string and the wheel. In real-world situations, these assumptions may not hold, and the answers may vary.