Centre of gravity and dynamics

In summary, the author is explaining that the CG (center of gravity) is a point that all the mass in an object can be thought of as existing. He states that the acceleration of this point is directly related to the external forces acting upon the object. The CG is also a point where the forces acting upon the object can be divided into two categories-internal and external.
  • #1
chandran
139
1
in a dynamics problem the example in a book shows a circular rod rotating about a pin at the end. Now the author says that the
cg of the rod is at a point and he draws an acceleration vector from cg towards the pin and says that it is the normal acceleration and a perpendicular component called tangential acceleration. My question is why these two acceleration vectors should be drawn from cg why not
from any other point in the rod and the problem solved
 
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  • #2
If the acceleration was to be on any part aside from the CM then there would be a torque about the center of mass. An acceleration at the CM gives pure translational accel.
 
  • #3
chandran said:
in a dynamics problem the example in a book shows a circular rod rotating about a pin at the end. Now the author says that the
cg of the rod is at a point and he draws an acceleration vector from cg towards the pin and says that it is the normal acceleration and a perpendicular component called tangential acceleration. My question is why these two acceleration vectors should be drawn from cg why not
from any other point in the rod and the problem solved
C.G.'s accelerations are directly related to the EXTERNAL forces acting upon the body.
The acceleration of any other point is related to the forces acting at that point (mass), whether those forces are external or internal to the body as a whole.
 
  • #4
What is the definition of a CG? It's a theoretical point that all of the mass can be thought of existing in an object. If you are looking for forces and only have an acceleration, shouldn't it seem that the accelerations would make the most sense to be applied at the point where all of the mass exists?
 

Related to Centre of gravity and dynamics

1. What is the definition of center of gravity?

The center of gravity is the point on an object where the weight of the object can be considered to act. It is the point at which the entire weight of the object can be concentrated, and it is the point where the object will balance in any orientation.

2. How is the center of gravity determined?

The center of gravity is determined by the distribution of mass within an object. It can be calculated by finding the weighted average of the positions of each particle of mass within the object. For simple objects with uniform density, the center of gravity can be found at the geometric center of the object.

3. How does the center of gravity affect an object's stability?

The lower an object's center of gravity, the more stable it will be. This is because a lower center of gravity means the weight of the object is more evenly distributed and less likely to tip over. Additionally, a wider base of support also increases an object's stability.

4. What is the relationship between center of gravity and dynamics?

The center of gravity plays a crucial role in an object's dynamics, or how it moves and responds to external forces. The position of an object's center of gravity determines how it will respond to different forces, such as gravity, friction, and torque. A stable center of gravity can also help an object maintain its balance when subjected to external forces.

5. Can the center of gravity be changed?

Yes, the center of gravity can be changed by altering the distribution of mass within an object. For example, adding weight to one side of an object will shift the center of gravity towards that side. This can affect the object's stability and dynamics, so it is important to consider the center of gravity when designing or modifying objects.

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