Angular Momentum of a candy dish

• al86
In summary, the conversation discusses a problem involving a rotating candy dish, or lazy susan, with a bug walking along its circumference. The bug has a mass of 35.9 g and is moving at a speed of 6.12 cm/s relative to the disk. The problem requires using the conservation of angular momentum to find the angular speed of the lazy susan, which is a uniform disk with a mass of 0.876 kg and a radius of 0.244 m.
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

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?

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.

1. What is angular momentum?

Angular momentum is a physical quantity that measures the amount of rotational motion an object has. It is the product of an object's moment of inertia and its angular velocity.

2. How is angular momentum related to a candy dish?

In the context of a candy dish, angular momentum refers to the rotational motion of the dish itself. As the dish spins, it has a certain amount of angular momentum.

3. How is angular momentum of a candy dish calculated?

The angular momentum of a candy dish can be calculated by multiplying its moment of inertia (a measure of how the mass is distributed around the axis of rotation) by its angular velocity (the rate at which it rotates).

4. What factors affect the angular momentum of a candy dish?

The angular momentum of a candy dish can be affected by its mass, moment of inertia, and angular velocity. Additionally, external forces such as friction or air resistance can also affect its angular momentum.

5. Why is angular momentum important in physics?

Angular momentum is important in physics because it is a conserved quantity, meaning it stays constant in a closed system. This principle is used in many real-world applications, such as spacecraft navigation and gyroscopes.

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