![]() ![]() Suppose I have two identical masses connected by a zero mass rod and I have this object near a massive object. But when would they be different? Here is an extreme example. In this post, these two locations are the same. The center of gravity is point in an object that you could use to model the motion due to gravitational forces. But what is the difference? The center of mass is just the mass weight sum of all the point masses that make up an object. I tried to always say "center of gravity" but in real life I often say "center of mass". What is Arnold made of? This is just like the Darth Vader post except with Arnold Schwarzenegger.Have you ever noticed how awkward it can be when someone tries to walk with one of these baby carriers-car seat things? Should dwarves stand in barrels? In this post, I look at the center of gravity for a dwarf in a floating barrel from the movie version of The Hobbit.It's the same case as this crane-tank thing expect Darth Vader doesn't fall over. How much does Darth Vader weigh? In this post, I look at the scene where Vader holds up a rebel soldier.Modeling the motion of a falling slinky.Here are some other examples of tipping or not tipping over with the center of gravity (for your reading pleasure). This is why you need to have the center of gravity in between the two support points (or directly over one of them) so that the object will not tip over. There is no way these two torques can cancel. Then both the gravitational force at the center of gravity and the ground pushing on the right tire create counterclockwise torques. The left tire exerts no torque about this point since the torque arm is zero. In this case it doesn't matter what point you calculate the torque about - but as an example, let's look at the left tire. Oh, you don't like that? You could do the same thing with the torque about any point. This would be balanced by the counterclockwise torque from the ground pushing on the right wheel. The gravitational force at the center of mass would cause a clockwise torque on the system. Let's look at that wheel on the left as the point about which we calculate the torque. But what about torque? In order for the crane to NOT tip over, the net torque about any point must be zero. Here is a diagram showing the forces on the system before it tips over.Ĭlearly the ground pushes up at the location of the tires and this total ground force must have the same magnitude as the total gravitational force. Instead of looking at the gravitational force and torque on all the individual masses in the crane plus tank system, I can just look at the center of gravity. Of course, I could make a similar calculation for the y and z-direction. And here is the definition of the center of gravity in the x-direction. It dropped out before because x 4 was zero, but it's more generic to have it in there. Notice that I put mass 4 back into the calculation. Where could I put this one gravitational force so that it gives the same torque about some point (point o in this case)? When dealing with torques, it's not just the magnitude of the force that matters but also the location. Clearly a net gravitational force of F = ( m 1 + m 2 + m 3 + m 4)g would give the same total gravitational force. What if I could use just ONE gravitational force instead of many? The key is that this force would have to give the same net force and the same net torque as the 4 individual gravitational forces. No one has time to calculate that many forces (it's too hard even for a computer). If I had just 12 grams of carbon, that would be more than 10 23 atoms that have gravitational forces on them. For real objects, there are more than 4 point masses. No one wants to deal with four gravitational forces. Net torque and net force are really all that we need to describe what happens to this thing. But what about the rest of the torque? All of the forces are perpendicular to the x-axis so that sin(θ) = 1. ![]() ![]() Both of these forces have a zero value for r since they both push AT this calculation point. ![]() If I am calculating the torque about an axis through mass number 4, then both the force, F and the gravitational force on mass 4 would have zero torque. In this case, the r is the distance from the point (or axis) that the torque is being calculated and θ the angle between r and the force. Torque should actually be described as a vector, but this definition will work here. ![]()
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