Is a Rigid Body Always Concentrated at its Center of Mass in Circular Motion?

In summary, when considering the pure rotation of a rigid body about a point, the body can be treated as a point object situated at its center of mass. This is because Newton's 2nd law for translation still applies in this scenario. However, there may be cases where this is not applicable, such as when dealing with moment of inertia.
  • #1
atavistic
106
0
When considering pure rotation of a rigid body about some point , then can we always consider the body to be concentrated in its centre of mass and use all force related equation treating it like a point object situated at it center of mass.? Why? Can anyone prove mathematically because there are many things like moment of inertia ,for e.g, for which we cannot do that.
 
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  • #2
BUMP please I really need this in a few hours.
 
  • #3
I'm not sure I understand your question. If you're asking whether Newton's 2nd law for translation applies--sure:

[tex]\Sigma F = ma_{cm}[/tex]

If that's not what you mean, please give a specific example of your concern.
 

1. What is circular motion of a rigid body?

Circular motion of a rigid body is when an object rotates around a fixed axis in a circular path. This type of motion is different from linear motion, where an object moves in a straight line.

2. What is the difference between circular motion and rotational motion?

Circular motion refers to the motion of an object in a circular path, while rotational motion refers to the spinning or turning motion of an object around its own axis. In circular motion, the object's distance from the axis remains constant, while in rotational motion, the object's shape or orientation changes over time.

3. What is the difference between uniform circular motion and non-uniform circular motion?

In uniform circular motion, the object moves around the circular path at a constant speed, meaning its linear velocity remains constant. In non-uniform circular motion, the object's speed changes along the circular path, resulting in a changing linear velocity.

4. What are the forces acting on an object in circular motion?

In circular motion, the object experiences a centripetal force, which is directed towards the center of the circular path, and keeps the object moving in a circular motion. This force can be provided by tension, gravity, or friction. The object may also experience a tangential force, which is perpendicular to the centripetal force and causes the object to speed up or slow down along the circular path.

5. How is angular velocity related to linear velocity in circular motion?

Angular velocity is a measure of how fast an object is rotating around an axis, while linear velocity is a measure of how fast an object is moving in a straight line. In circular motion, the angular velocity and linear velocity are related by the formula v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the distance from the object to the axis of rotation.

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