Look at your first equation. It defines the integral of F (in your sense) as a change in momentum.Kyuutoryuu said:
Kyuutoryuu said:
(Change in momentum is the area under a force against time curve.)
(Force is the time derivative of momentum.)
Using separation of varibles, you get Fdt=dp. Integrate both sides, you get that the integral of Force with respect to time is equal to p. This seems to imply that p, momentum, is equal to change in momentum?
Impulse and momentum are both physical quantities related to motion, but they have different definitions. Impulse is the change in momentum over a period of time, while momentum is the product of an object's mass and velocity. In other words, impulse measures the force applied to an object over time, while momentum measures the quantity of motion an object has.
In a system of multiple objects, the total impulse and momentum can be calculated by adding up the individual impulses and momenta of each object. This is known as the principle of conservation of momentum, which states that the total momentum of a closed system remains constant.
Some common errors in deriving equations for impulse and momentum include using incorrect units, not taking into account the direction of the force or velocity, and not properly applying the principles of conservation of momentum. It is important to carefully check all calculations and make sure they align with the principles and definitions of impulse and momentum.
To ensure the accuracy of your derivations, it is important to check for consistency with known equations and principles, such as the laws of motion and the principle of conservation of momentum. You can also double-check your calculations and units to make sure they are correct.
The equations for impulse and momentum are derived from the laws of motion, which apply to linear systems. Non-linear systems, such as those involving rotational motion, may require different equations and principles. It is important to consider the specific characteristics of the system in question when using impulse and momentum equations.