# Rotation of Object around it's centre of mass

• mahi.aw
In summary, the conversation is about rotating an object around its center of mass instead of the origin of Cartesian coordinates. One method suggested is to translate the object's center of mass to the origin, rotate it, and then translate it back. However, this may lead to more calculations and affect the program's performance. The other person suggests a method that involves only 4 multiplications and 6 additions. The conversation ends with someone asking for clarification on the formula and mentioning that they are not using matrices in their calculations.
mahi.aw
Hi all I am new here!

can anyone tell me how can i rotate the object around it's center of mass and not the origin of Cartesian co-ordinates(0,0)..

1. translate the object so its center of mass is at the origin
2. rotate it.
3. translate it back.

It's sounds good...

But if i do like this way i think i need to do more and more calculations,,which ultimately leads to reduce performance of my program..

is there way to rotate it without translating the object center of mass to it's origin??

mahi.aw said:

It's sounds good...

But if i do like this way i think i need to do more and more calculations,,which ultimately leads to reduce performance of my program..

is there way to rotate it without translating the object center of mass to it's origin??

The method it's been suggested is very quick for a computer as it implies something like only 4 multiplications and 6 additions.

Any other method leads certainly to more complex equations.

Hi Quinzio,

But i did not get the idea of 4 multiplications and 4 additions??
could you please elaborate on it?

Then I think you need the complete formula (this is not the homework section, btw), then you can elaborate it.

$$\left\{\begin{matrix} {x}'= (x-x_M)cos \alpha - (y-y_M)sin \alpha+x_M \\ {y}'= (y-y_M)cos \alpha + (x-x_M)sin \alpha+y_M \end{matrix}\right.$$

i know that...but i asked just b/c am not using any matrices in calculation..

thanks & regards

## 1. What is rotation of an object around its center of mass?

Rotation of an object around its center of mass is the motion of an object along an axis passing through its center of mass. This type of rotation is also known as rotational motion and is seen in many everyday objects, such as a spinning top or a rotating wheel.

## 2. How does rotation around the center of mass affect an object?

Rotation around the center of mass affects an object by changing its orientation and direction of motion. It can also cause the object to experience centrifugal and centripetal forces, depending on the direction of the rotation.

## 3. What is the relationship between the moment of inertia and rotation around the center of mass?

The moment of inertia of an object is a measure of its resistance to rotational motion. When an object rotates around its center of mass, the moment of inertia plays a critical role in determining its rotational speed and the amount of torque needed to change its rotational motion.

## 4. What factors affect the rotation of an object around its center of mass?

The rotation of an object around its center of mass is affected by various factors, including the object's shape, mass distribution, and external forces acting upon it. These factors can determine the object's moment of inertia and the direction and speed of its rotation.

## 5. How is the conservation of angular momentum related to rotation around the center of mass?

The conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. This principle applies to rotation around the center of mass, where any changes in the object's rotational motion must be balanced by an equal and opposite change in the rotational motion of the surrounding objects or forces.

• Mechanics
Replies
35
Views
3K
• Mechanics
Replies
2
Views
715
• Mechanics
Replies
1
Views
682
• Mechanics
Replies
10
Views
2K
• Mechanics
Replies
47
Views
4K
• Mechanics
Replies
12
Views
4K
• Mechanics
Replies
2
Views
171
• Mechanics
Replies
133
Views
9K
• Mechanics
Replies
1
Views
879
• Classical Physics
Replies
141
Views
5K