Angular Momentum of a candy dish

[al86]

Homework Statement

A candy dish that rotates is called a lazy susan. This lazy susan is a uniform disk (mass 0.876 kg, radius 0.244 m), rotating about the center of the disk on a frictionless bearing. Suppose a large bug of mass 35.9 g sits at rest at on the edge of the empty lazy susan, which is initially at rest. The bug now begins to walk along the circumference of the disk at 6.12 cm/s relative to the disk. Find ω, the angular speed of the lazy susan.

Homework Equations

I just need a hint... based on the information provided i think i need to work my way through the conservation of angular momentum.. ... any suggestion

The Attempt at a Solution

 

[Hootenanny]

Conservation of angular momentum is indeed the way to go.

In this case what must the total angular momentum of the system (bug and disc) be?

What is the angular momentum of the bug?

Therefore, what must be the angular momentum of the disc?

 

[thomate1]

To find the angular speed of the lazy susan, we can use the equation ω = v/r, where v is the tangential velocity of the bug and r is the radius of the disk. In this case, v = 6.12 cm/s and r = 0.244 m. Plugging these values into the equation, we get ω = 6.12 cm/s / 0.244 m = 25.0 rad/s. This is the angular speed of the lazy susan.

To further analyze the system, we can also use the conservation of angular momentum, which states that the initial angular momentum of a system is equal to the final angular momentum. In this case, the initial angular momentum is zero since the lazy susan and the bug are both at rest. As the bug starts walking, it gains angular momentum, but the lazy susan will also start rotating in the opposite direction to conserve the overall angular momentum of the system.

To calculate the final angular momentum, we can use the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular speed. The moment of inertia for a uniform disk rotating about its center is 1/2 * mr^2, so in this case, I = 1/2 * 0.876 kg * (0.244 m)^2 = 0.0107 kgm^2. Plugging this into the equation, we get L = 0.0107 kgm^2 * 25.0 rad/s = 0.2675 kgm^2/s. This is the final angular momentum of the system, which is equal to the initial angular momentum of zero.

Overall, the angular momentum of the candy dish, or lazy susan, changes as the bug starts walking, but the total angular momentum of the system remains constant due to conservation of angular momentum.