Conservation of Angular Momentum in a Rotating System

In summary, a circular turntable with a mass of 2.0 kg and a radius of 6.0 inches is rotating freely at 66 2/3 rpm. A 500 gram blob of clay is dropped on the disk 4.0 inches from the center. To find the resulting angular speed, the clay can be treated as a point mass and the turntable as a disk. The moment of inertia of the system will play a role in determining the resulting angular speed. The angular speed will be the sum of the initial angular speed of the turntable and the angular speed caused by the added mass of the clay. Conservation of angular momentum is a relevant conservation law to consider in this problem.
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Homework Statement



A circular turntable of mass 2.0 kg and radius 6.0 inches is rotating freely at 66 2/3 rpm. If a 500 gram blob of clay is dropped on the disk at a distance of 4.0 inches from the center, what is the resulting angular speed of the system? Treat the clay as a point mass (I = MR^2) and the turntable as a disk.

Homework Equations

The Attempt at a Solution


I understand the resulting angular speed will be the sum of the two. But what does moment of inertia have to do with it??
 
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What do you mean about the angular speed being the sum of the two? Doesn't sound right.
What relevant conservation law do you know?
 

1. What is resulting angular speed?

Resulting angular speed, also known as angular velocity, is the measure of how quickly an object is rotating about a fixed point. It is usually expressed in radians per second (rad/s).

2. How is resulting angular speed calculated?

The formula for resulting angular speed is ω = Δθ/Δt, where ω is the angular speed, Δθ is the change in angle over a period of time, and Δt is the change in time. This can also be written as ω = 2πf, where f is the frequency of rotation in hertz.

3. What is the difference between resulting angular speed and tangential speed?

Resulting angular speed measures the rate of rotation, while tangential speed measures the rate of change of an object's linear position. Essentially, resulting angular speed is how fast something is spinning, while tangential speed is how fast something is moving in a straight line.

4. How does resulting angular speed affect rotational motion?

Resulting angular speed is directly proportional to rotational motion. This means that as the resulting angular speed increases, so does the rotational motion. This can also be seen in Newton's first law of motion, which states that an object in motion will remain in motion at a constant resulting angular speed unless acted upon by an external force.

5. How is resulting angular speed used in real life?

Resulting angular speed is used in many real-life applications, such as in the design and functioning of engines, turbines, and propellers. It is also used in the study of celestial bodies and their movements, as well as in sports such as figure skating and gymnastics where rotational motion is important.

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