A woman with a mass of 50kg is standing on the rim of a large disk that is rotating at an angular velocity of .50 rev/s about an axis through its center. The disk has a mass of 110kg and a radius of 4.0m. Calculate the magnitude of the total angular momentum of the woman-plus-disk system. (Assume that you can treat the woman as a point.)

Look up the moment of inertia of a disc. Call it Id. The angular momentum of the disc is Id w. The added angular momentum of the woman is Mw* R^2 w.
Mw is the mass of the woman. R is the radius of the disc

The total angular momentum is
(Id + Mw*R^2) w

w is the angular velocity in radians/s. Get it from number of revolutions per s.

Please show your work.

1280

Given information:

Mass of woman (Mw) = 50 kg
Mass of disk (Md) = 110 kg
Radius of disk (R) = 4.0 m
Angular velocity (w) = 0.50 rev/s

Step 1: Convert the angular velocity from revolutions per second to radians per second.
To do this, we need to use the conversion factor 2π rad = 1 rev.
So, w = (0.50 rev/s) × (2π rad/1 rev) = π rad/s.

Step 2: Calculate the moment of inertia of the disk (Id).
The moment of inertia of a disk is given by the formula: Id = (1/2) Md R^2.
Plugging in the values, we get:
Id = (1/2) × (110 kg) × (4.0 m)^2 = 880 kg·m^2.

Step 3: Calculate the angular momentum of the disk (Ld).
The angular momentum of the disk is given by the formula: Ld = Id × w.
Plugging in the values, we get:
Ld = (880 kg·m^2) × (π rad/s) = 880π kg·m^2/s.

Step 4: Calculate the added angular momentum of the woman (Lw).
The added angular momentum of the woman is given by the formula: Lw = Mw × R^2 × w.
Plugging in the values, we get:
Lw = (50 kg) × (4.0 m)^2 × (π rad/s) = 800π kg·m^2/s.

Step 5: Calculate the total angular momentum of the woman-plus-disk system (Lt).
The total angular momentum is the sum of the angular momentum of the disk and the added angular momentum of the woman.
Thus, Lt = Ld + Lw = 880π kg·m^2/s + 800π kg·m^2/s = 1680π kg·m^2/s.

Therefore, the magnitude of the total angular momentum of the woman-plus-disk system is 1680π kg·m^2/s.

To calculate the magnitude of the total angular momentum of the woman-plus-disk system, we need to follow these steps:

1. Look up the moment of inertia of a disc. The moment of inertia of a disc can be calculated using the formula: Id = (1/2) * m * r^2, where m is the mass of the disc and r is its radius. In this case, the mass of the disc is given as 110 kg and the radius is given as 4.0 m. Plugging in these values, we can calculate the moment of inertia of the disc: Id = (1/2) * 110 kg * (4.0 m)^2.

2. Calculate the angular velocity in radians per second. The given angular velocity is 0.50 rev/s (revolutions per second). To convert this to radians per second, we need to multiply by 2π, since one revolution is equal to 2π radians. Therefore, the angular velocity in radians per second is: w = 0.50 rev/s * 2π rad/rev.

3. Calculate the additional angular momentum contributed by the woman. The woman can be treated as a point, and her additional angular momentum can be calculated using the formula: Mw * R^2 * w, where Mw is the mass of the woman and R is the radius of the disc. In this case, the mass of the woman is given as 50 kg and the radius of the disc is given as 4.0 m. Plugging in these values, we can calculate the additional angular momentum contributed by the woman: Mw * R^2 * w = 50 kg * (4.0 m)^2 * (0.50 rev/s * 2π rad/rev).

4. Calculate the total angular momentum. The magnitude of the total angular momentum is the sum of the angular momentum of the disc (Id * w) and the additional angular momentum contributed by the woman (Mw * R^2 * w). Therefore, the total angular momentum can be calculated as: (Id + Mw * R^2) * w.

Now you have all the necessary information and formulas to calculate the magnitude of the total angular momentum of the woman-plus-disk system. Simply plug in the values and perform the calculations to get the final result.

dis diq