Someone please help me! I've been stuck on this problem for a while now and i can't figure it out!

A disk with mass m = 5.2 kg and radius R = 0.44 m hangs from a rope attached to the ceiling. The disk spins on its axis at a distance r = 1.59 m from the rope and at a frequency f = 18.6 rev/s (with a direction shown by the arrow).
1.What is the magnitude of the angular momentum of the spinning disk?
2.What is the torque due to gravity on the disk?
3.What is the period of precession for this gyroscope?

To answer these questions, let's go step by step:

1. The magnitude of the angular momentum of the spinning disk can be calculated using the formula:

L = I * ω

where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

The moment of inertia for a disk rotating around its axis of symmetry is given by:

I = (1/2) * m * R^2

Substituting the given values for mass and radius, we can calculate the moment of inertia:

I = (1/2) * 5.2 kg * (0.44 m)^2

Once we have the moment of inertia, we can calculate the angular momentum using the formula:

L = I * ω

where ω is given by the frequency of rotation, which is 18.6 rev/s. Since 1 revolution (rev) is equal to 2π radians, we can convert the frequency to angular velocity using the conversion factor:

ω = 18.6 rev/s * 2π rad/rev

Once we have ω, we can calculate the angular momentum:

L = I * ω

2. The torque due to gravity on the disk can be calculated using the formula:

τ = m * g * r

where τ is the torque, m is the mass of the disk, g is the acceleration due to gravity, and r is the distance from the point of rotation to the point where the force is applied.

Substituting the given values, we can calculate the torque:

τ = 5.2 kg * 9.8 m/s^2 * 1.59 m

3. The period of precession for the gyroscope can be calculated using the formula:

T = (2π) / ω_p

where T is the period of precession, and ω_p is the angular precession velocity.

The angular precession velocity can be calculated using the formula:

ω_p = (m * g * R) / (L * ω)

Substituting the given values, we can calculate the angular precession velocity:

ω_p = (5.2 kg * 9.8 m/s^2 * 0.44 m) / (L * ω)

Once we have the angular precession velocity, we can calculate the period of precession using the formula:

T = (2π) / ω_p

Now, you have the step-by-step explanation on how to calculate each of the answers. I suggest you plug in the given values and perform the calculations to get the final results. If you encounter any issues or have further questions, feel free to ask!