Dynamics the why of motion

Dynamics considers the forces that affect the motion of moving objects and systems. These laws provide an example of the breadth and simplicity of principles under which nature functions.

They are also universal laws in that they apply to similar situations on Earth as well as in space. This transition was characterized by a revolutionary change in the way people thought about the physical universe.

For many centuries natural philosophers had debated the nature of the universe based largely on certain rules of logic with great weight given to the thoughts of earlier classical philosophers such as Aristotle — BC. Among the many great thinkers who contributed to this change were Newton and Galileo.

Figure 2. It proposed scientific laws that are still used today to describe the motion of objects. The experiment is repeated with various hanging masses causing different pulling forces and the acceleration is measured from the recorded motion. Graphing the experimental values for the applied force versus the resulting accelerations produces a straight line graph to within experimental accuracy.

The slope is equal to the mass of the moving system to within experimental error. Assuming that the bullet has constant acceleration over the 0.

We could sketch a v vs t graph where we know the area beneath is the distance 0. Knowing the time for the bullet to accelerate in the rifle, we can find the acceleration and then the force:. Newton's Third Law of Motion is often stated as "For every action there is an equal and opposite reaction. More plainly put, if object A applies a force on object B, then B will apply an equal force on A in the opposite direction.

Consider a car traveling. If the car accelerates due to a N force on it there is another object that experiences a N force in the opposite direction. In this case, it would be the road. Similarly, an aircraft accelerates because it applies a backward force on the air via a propeller or turbine , and the air applies a forward force on the aircraft.

Experimentally, it is verified that this elongation is proportional to the force by successively adding several identical weights. Once calibrated, this spring force gauge can be used to measure different forces. This is none other than the result of the atmospheric pressure forces acting all around the envelope: due to the pressure decrease with altitude, the pressure is higher at the bottom of the envelope than at the top, which translates into a net upward force.

It is thanks to this balance that air plots, or water plots within a basin, do not fall to the ground under the influence of gravity. When the air is heated, its density and therefore the mass of a given volume decreases, while the pressure remains unchanged because it is controlled by the weight of the surrounding air. The balance is then disrupted leading to a vertical acceleration of the balloon.

In the atmosphere, an air mass heated locally by solar radiation will also tend to rise: this is the principle of convection. Figure 2. The equilibrium shape is such that at each wire intersection the vector sum of the forces is equal to zero. Each beam element is represented by a wire, and its mass simulated by a weight. The tension force on a yarn is necessarily aligned with the yarn. In the actual inverted configuration, the corresponding force will then be a compression force aligned along the beam, which guarantees its mechanical strength.

More generally, the balance of forces must be expressed as vectors , which is the basis for calculating structures in architecture, see Figure 2.

For each material point, for example the intersection node of the wires, the vector sum of the forces must cancel each other out at equilibrium, as shown in Figure 3a.

An extended object, for example a solid , is described in physics as a set of material points held together by internal forces. These forces are to be distinguished from external forces such as weight or forces of contact with other objects. The sum of the internal forces is cancelled out by the principle of action and reaction , so that equilibrium requires the cancellation of the sum of the external forces.

But the equilibrium condition of an extended object also requires the cancellation of the total moment of the forces, to avoid its rotation. The moment of a force with respect to an axis is defined as the product of the force, projected perpendicular to the axis, by the distance to the axis. The classic example is the lever shown in Figure 3b.

It is usual to consider the moments in relation to the axis of the lever, because the moment of the reaction force R of the ground cancels itself out. However, the same result could be obtained by calculating the moment with respect to any mathematical axis, adding the moment of the reaction R , which is an equal vector and opposite to the sum of the two forces F1 and F2.

In the absence of force, an object moves at a uniform speed, this is the principle of inertia first stated by Galileo This principle was not very intuitive at the time, because in everyday life any movement tends to stop in the absence of effort. This deceleration negative acceleration is now attributed to friction forces, which are opposed to speed.

In fact, we consider the limit of a very short time interval. For a sufficiently high horizontal velocity, the curvature of the Earth must then be taken into account, and the circular motion of a satellite is obtained, see Figure 4. Force is a vector quantity, which means that direction matters. Use positive values for forces that point in the preferred direction and negative values for forces that point in the opposite direction.

If a problem is two dimensional, pick two preferred directions at right angles — something like up and to the right. Pick preferred directions that make your life easy.

The laws of physics do not care if you call right positive or left positive. Space, in the mathematical sense, is isotropic. It measures the same in all directions. Newton's second law of motion describes how net force, mass, and acceleration are related. Basically, net force causes acceleration and mass resists it. The best way to write that is not with words but with symbols.

Something like this…. Take the unexceptional example of an unexceptional bicycle being unexceptionally pedaled down an unexceptional flat, level road in an unexceptional manner. What are the forces acting on the bicycle and rider together as a whole? Start with the obvious. Everything has weight and weight points down.

The bicycle is on a solid surface so there's a normal force pointing normal to that surface. The surface is level so the normal direction is up.