# Rotational dynamics, semicircular arc

• Saitama
In summary, the homework equation states that the angular acceleration is proportional to the torque applied to the object. If you want to find the angular acceleration of an object, you need to first find the torque applied to it.
Saitama

(see attachment)

## The Attempt at a Solution

Do I need to take torque about C here?

Any help is appreciated, Thanks!

#### Attachments

• semicircular arc.jpg
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Do I need to take torque about C here?
How else would you find the angular acceleration?

Simon Bridge said:
How else would you find the angular acceleration?

I asked this because I am sure this would involve integrals and before doing the maths, I want to be sure if I am heading in the right direction.

If you can only think of one way to do a problem, it is worth a try: give it a go.
Everything involves an integral if you don't already know the result.

But it can help to have a think about the problem before starting:
* If ##\beta=0##, what is the initial angular acceleration?
* How does the total mass vary with ##\beta##?
* How does the location of the center of mass vary with ##\beta##?

Simon Bridge said:
If you can only think of one way to do a problem, it is worth a try: give it a go.
Everything involves an integral if you don't already know the result.

But it can help to have a think about the problem before starting:
* If ##\beta=0##, what is the initial angular acceleration?
* How does the total mass vary with ##\beta##?
* How does the location of the center of mass vary with ##\beta##?

I have solved the problem, I had trouble because I misinterpreted the problem. It looked to me like a semicircular arc but it isn't. Thanks!

Pranav-Arora said:
I have solved the problem, I had trouble because I misinterpreted the problem. It looked to me like a semicircular arc but it isn't. Thanks!
Yes, it's a poor drawing. The point where those angles meet doesn't look like it's supposed to be the centre of the arc.

## 1. What is rotational dynamics?

Rotational dynamics is the branch of physics that studies the motion of objects that rotate around an axis. This includes understanding concepts such as torque, angular velocity, and angular momentum.

## 2. What is a semicircular arc?

A semicircular arc is a half circle, or a portion of a circle that has an angle of 180 degrees. It is often used in rotational dynamics to calculate the motion of a rotating object along a circular path.

## 3. How is rotational dynamics related to semicircular arcs?

Rotational dynamics is closely related to semicircular arcs because objects that rotate around an axis follow a circular path, which can be represented as a semicircular arc. By understanding rotational dynamics, we can predict the motion of an object along a semicircular arc.

## 4. What is the importance of semicircular arcs in rotational dynamics?

Semicircular arcs are important in rotational dynamics because many real-world systems involve objects rotating along a circular path. By understanding the principles of semicircular arcs, we can better understand the behavior of rotating objects and make predictions about their motion.

## 5. What are some applications of rotational dynamics and semicircular arcs?

Rotational dynamics and semicircular arcs have many practical applications, such as in the design of engines, turbines, and other rotating machinery. They are also used in sports, such as calculating the trajectory of a thrown discus or the spin of a figure skater. In addition, rotational dynamics is important in understanding the motion of celestial bodies, such as planets and stars.

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