Angular momentum of a rigid body

[DH214]

A 0.15 meter long, 0.15 kg thin rigid rod has a small 0.22 kg mass stuck on one of its ends and a small 0.080 kg mass stuck on the other end. The rod rotates at 1.7 rad/s through its physical center without friction. What is the magnitude of the angular momentum of the system taking the center of the rod as the origin? Treat the masses on the ends as point masses

 

[hage567]

What have you tried so far?

 

[thomate1]

The angular momentum of a rigid body is a measure of its rotational motion and is calculated by multiplying the moment of inertia by the angular velocity. In this scenario, we have a thin rigid rod with two point masses attached to its ends, rotating at a constant speed of 1.7 rad/s through its center without friction. We can calculate the moment of inertia of the system by using the formula I = MR^2, where M is the mass and R is the distance from the axis of rotation to the point mass.

For the mass on one end of the rod, we have M = 0.22 kg and R = 0.075 m (half of the rod's length). Plugging these values into the formula, we get a moment of inertia of 0.0010125 kg*m^2. Similarly, for the mass on the other end, we have M = 0.080 kg and R = 0.075 m, giving a moment of inertia of 0.00036 kg*m^2.

To find the total moment of inertia for the system, we add these two values together, giving us a total moment of inertia of 0.0013725 kg*m^2. Now, we can calculate the angular momentum by multiplying the moment of inertia by the angular velocity, giving us a final value of 0.00233 kg*m^2/s.

It is important to note that the center of the rod is chosen as the origin for the calculation of angular momentum because it is the point where the rotation occurs without any external forces or friction. This allows us to simplify the calculation and treat the masses on the ends as point masses.

In conclusion, the magnitude of the angular momentum of the system, taking the center of the rod as the origin, is 0.00233 kg*m^2/s. This value represents the rotational motion of the rigid body and can be used to analyze the system's behavior and dynamics.