Centre of Gravity
While they are actually slightly different, center of mass and the center of gravity can be used interchangeably, and are considered the same, when the gravitational field is uniform.
Weight is the mass times the acceleration due to gravity, 9.8m/s2
Test it out
Tap the diagram for more information and click on the buttons to change a component and see what happens!
Increase m1m_1 Weight
Use Plumb Line
Tilt Vehicles
Example calculations
In order to work with Centre of Gravity, mechanical engineers need to understand and work with a variety of calculations. Here are just a few:
Centre of Gravity by Moment (in x, y and z co-ordinates):
xˉ=Σx^WΣW  yˉ=Σy^WΣW  zˉ=Σz^WΣW\bar x = \frac{\Sigma \hat x W}{\Sigma W} \ \ \bar y = \frac{\Sigma \hat y W}{\Sigma W} \ \ \bar z = \frac{\Sigma \hat z W}{\Sigma W}
Centre of Gravity on Car (CG):
CG distance from front axle=weight of rear axle×wheelbasetotal vehicle weightCG\ distance\ from\ front\ axle = \frac{weight\ of\ rear\ axle \times wheelbase}{total\ vehicle\ weight}
Note: Vehicle must be perfectly horizontal to get the accurate reading
Centre of GravityCGCG
Distance to X Co-ordinateXX
Force of GravityFGF_G
Centrifugal ForceFF
Height of Centre of Gravityhh
Width of Basebb
When most people buy a car, they don't really ask about its Centre of Gravity, but for mechanical engineers and manufacturers in the automotive industry, this area is an important parameter to help analyse and improve a car's performance. Factors that depend on centre of gravity include stability, braking efficiency, handling and safety.
With any solid object, the centre of gravity is the point at which all the object's weight is concentrated. In order to balance an object, all the weight of the item must be evenly distributed around this point, with all sides in balance.
For example, if you were to balance a fork on your finger, you wouldn't try to balance it in at centre of the full length, but rather closer to the head where the prongs and all the weight is sitting. In this way, most of the handle will stick out, but the handle's weight will be equal to that of the prongs. From this, we can see that the centre of gravity would then be closer to the head of the fork.
With cars, centre of gravity is an important consideration when turning the vehicle. When a car is turning, the momentum of the vehicle pulls the centre of gravity towards the direction of the turn. If the weight is then incorrectly distributed the vehicle can roll over.
Imagine a bus going around a corner - if it goes too fast, and tips the centre of gravity off its base, the bus is at risk of falling over! A Lamborghini however has a lower centre of gravity because of its low height and wide base. This makes it more stable, and better at sticking to the road better at high speeds. If it were to tip at all, it's also more likely to fall back into position, rather than completely fall over.
Practice Questions
Test your new knowledge on centre of gravity by answering these questions.
1. A simple way to find the centre of gravity on a strange object is:
2. Centre of gravity means:
3. What is a centroid?