# Rotational momentum (conservation problems)

• thatguy14
In summary, the conversation discusses a rigid structure consisting of a circular hoop and a square made of four thin bars, rotating at a constant speed with a period of 2.5 seconds. The question asks for the structure's rotational inertia and angular momentum about the axis of rotation, assuming specific values for radius and mass. The conversation also mentions the parallel axis theorem and the difficulty in finding the rotational inertia of the square. It is suggested to use the moments of inertia for a thin rod, even though the question specifies thin bars.
thatguy14
1.A rigid structure consisting of a circular hoop (on the right) of Radius R and mass m, and a square (on the left) made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a verticle axis, with a period of rotation of 2.5 s. Assuming R = 0.50m and m = 2.0 kg, calculate (a) the structures rotational inertia about the axis of rotation and (b) its angular momentum about that axis

There is a picture associated with the question but i can't upload it. Basically on the left is a square then right to the right of tht is a circle and inbetween the 2 there is a line drawn shoing the axis of rotation, the square is touching the circle.

2. Rotational inertia for the hoop = 1/2 MR^2
Parallel axis theorm = Icom + MH^2
I don't know how to find the rotational inertia of the square that is composed of 4 thin bars each of length R. The rotational inertia equation for the hoop was already given to us in a previous table in the book, but nothing for a thin rod rotating about its axis type of thing.
L = Iw w=(omega)

3. i couldn't do anything for this question as i couldn't find the rotational inertia of the square, I don't know how to.

I can't really picture what the system looks like, but you should be able to find the moment of inertia of the square as the combination of 4 bars (you should be able to look this up, or calculate it yourself) using the parallel axis theorem

hi i did look those up but the problem with it is that the questions usually tell you what to assume the thing is. It says thin bars not rods and it doesn't say to assume rods. So i asnt sure if there was something i was missing.

Also for all the moments of inertia of the rods that are parallel to the axis of rotation, there is no specified equation for the a thin rod with the axis of rotation down the rod; there's only perpendicular.

---- |
| || This is kind of what the diagram looks like
| || Except in this spot there is a circle that touches the axis of rotation
---- |

I don't know i that helps.

edit: seems it doesn't keep the formatting correclty. Ill try to get the image online so you can see it

So they don't give dimensions of the bars (other than length)? My guess is the moment of inertia will be the same as for a rod since the other dimensions are very small so they can be ignored. This also means that the moment of inertia around the rod's axis is basically 0, but you can still apply the parallel axis theorem.

## 1. What is rotational momentum?

Rotational momentum, also known as angular momentum, is a physical quantity that measures the rotational motion of an object. It is a vector quantity that takes into account the mass, velocity, and the distance of an object from an axis of rotation.

## 2. How is rotational momentum conserved?

According to the law of conservation of angular momentum, the total angular momentum of an isolated system remains constant. This means that the total rotational momentum before an event must be equal to the total rotational momentum after the event, as long as there are no external torques acting on the system.

## 3. What are some real-life examples of rotational momentum?

Some common examples of rotational momentum include spinning tops, rotating planets, and the motion of a spinning ice skater. Other examples include the rotation of a bicycle wheel, the movement of a spinning gyroscope, and the rotation of a ceiling fan.

## 4. How does rotational momentum differ from linear momentum?

Rotational momentum involves the rotation of an object around an axis, while linear momentum involves the straight-line motion of an object. Rotational momentum takes into account the mass, velocity, and distance from an axis of rotation, while linear momentum only considers the mass and velocity of an object.

## 5. How is rotational momentum used in engineering and technology?

Rotational momentum plays a crucial role in many engineering and technological applications. It is used in designing and analyzing rotating machinery, such as turbines and motors. It is also important in the design of vehicles and spacecraft, as well as in the development of new technologies such as gyroscopes and flywheels.

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