Angular Momentum of Spinning Wheel System

[BraedenP]

Homework Statement

Two gerbils run in place with a linear speed of 0.55m/s on an exercise wheel that is shaped like a hoop. Find the angular momentum of the system if each gerbil has a mass of 0.22kg and the exercise wheel has a radius of 6.5cm and a mass of 5.0g.

Homework Equations

$$L=rmv\sin(\theta)$$

The Attempt at a Solution

Basically, I just plugged in values for the variables in the above equation, except for the mass. I know that, since the gerbils aren't moving anywhere or going around the circumference of the wheel, they're not contributing to the angular momentum of the system.

However, I assume that they are adding mass to the system, so that should be taken into consideration when finding the answer. Thus, I calculated as follows:

$$L=0.065m \cdot (2 \cdot 0.22kg + 0.005kg) \cdot 0.55m/s \cdot sin(90)$$

$$L=0.0159 = 1.6 \cdot 10^{-2} kg \cdot m^2/s$$

Is that the proper way to do it? I just want to make sure that the mass of the gerbils should be included despite them being in the air part of the time as they run.

Thanks!

 

[anathema]

Hi there,

Yes, you are correct in including the mass of the gerbils in your calculation of angular momentum. Although they may not be physically touching the exercise wheel, their mass is still a part of the system and therefore contributes to the overall angular momentum.

Your calculation looks correct, but just a small note - when using the equation L=rmv sin(theta), the angle theta should be the angle between the position vector and the velocity vector. In this case, since the gerbils are running in place, the angle between their position and velocity vectors would be 90 degrees, so you would use sin(90) in your calculation.

Overall, good job on your solution! Keep up the good work.