Centre of mass vs. centre of gravity

In summary, when considering a symmetrical solid body, its center of mass is typically located at its geometric center. This is based on the assumption that the body has a uniform density, with mass varying in proportion to volume. However, when this same body is moved from one gravitational field (such as Earth) to another (such as Jupiter), it becomes harder to tip over if it is standing on its base. This is because for a body to tip over, the vertical line passing through its center of gravity must fall outside the base. In this stronger gravitational field, the center of gravity is lower compared to the center of mass on Earth. The question then arises if there is a formula for calculating the center of gravity in different fields relative to
  • #1
Kacker
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consider a symmetrical solid body. we say its centre of mass is at its geometric centre. that is, for uniform density we've taken mass to vary exactly as volume. now when the same body is taken from a place of gravitational field A to gravitational field B. say from the Earth to jupiter, this body (consider it to be a cone) would be harder to tip over were it standing on its base. that is because , for a body to tip over, the vertical line through the centre of gravity should pass outside the base. the geometry of the body unchanged, we say its centre of gravity is lowered in this stronger field. is there a formula by which we can calculate the centre of gravity in particular fields in relation to those in others?. I am assuming we take centre of gravity and centre of mass to coincide on Earth for convinience's sake.
 
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The centre of mass and centre of gravity are two concepts that are closely related but not identical. The centre of mass is the point at which the mass of an object is evenly distributed in all directions, while the centre of gravity is the point at which the gravitational force acting on an object can be considered to be concentrated.

In a symmetrical solid body, the centre of mass is at its geometric centre, as stated in the content. This is because the mass is evenly distributed throughout the body. However, when the same body is taken to a place with a stronger gravitational field, such as from Earth to Jupiter, the centre of gravity will shift. This is because the gravitational force acting on the body is stronger, causing the centre of gravity to be pulled towards the source of the gravitational field.

In the example given of a cone, the centre of gravity would be lowered in the stronger gravitational field of Jupiter. This means that the vertical line through the centre of gravity would pass closer to the base of the cone, making it harder to tip over. This is because the gravitational force acting on the cone is stronger, making it more stable.

To calculate the centre of gravity in different gravitational fields, there is a formula known as the gravitational torque formula. This formula takes into account the mass and distance of an object from the source of the gravitational field to determine the centre of gravity. However, this formula can become more complex when dealing with non-uniform gravitational fields, such as those found on planets with varying densities.

In general, it is safe to assume that the centre of gravity and centre of mass coincide on Earth for convenience's sake. However, in situations where the gravitational field is significantly different, it is important to take into account the shift in the centre of gravity. This is especially important in fields such as astrophysics, where understanding the distribution of mass and gravitational forces is crucial in studying celestial bodies.
 

1. What is the difference between the centre of mass and centre of gravity?

The centre of mass is the point at which the entire mass of an object is considered to be concentrated, while the centre of gravity is the point at which the weight of the object can be considered to act. In most cases, the centre of mass and centre of gravity are at the same location, but they can differ depending on the distribution of mass and the effects of gravity.

2. How do you calculate the centre of mass and centre of gravity?

The centre of mass can be calculated by finding the weighted average of the positions of all the particles that make up an object. The centre of gravity can be calculated by taking into account the mass and position of each particle, as well as the force of gravity acting on each particle.

3. Can the centre of mass and centre of gravity be outside of an object?

Yes, the centre of mass and centre of gravity can be outside of an object if the distribution of mass within the object is uneven. This can happen, for example, if an object has a hollow or irregular shape.

4. How does the centre of mass and centre of gravity affect an object's stability?

The position of the centre of mass and centre of gravity can greatly affect an object's stability. If the centre of mass is located directly above the base of support, the object will be stable. However, if the centre of mass is located outside of the base of support, the object will be less stable and may tip over.

5. How do the centre of mass and centre of gravity relate to rotational motion?

The location of the centre of mass and centre of gravity can affect an object's rotational motion. If the centre of mass and centre of gravity are aligned, the object will not experience any torque and will not rotate. However, if the centre of mass and centre of gravity are not aligned, the object will experience torque and will rotate around a fixed axis.

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