Understanding the implications of a momentum equation

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In summary: Therefore, the total momentum of a system is constant.In summary, the rate of change of total momentum in a system with respect to time is zero, which means that the total momentum of the system is constant. This is because the primitive function of zero is a constant, signifying that the function does not change with time.
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gibberingmouther
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Homework Statement



the rate of change of the total momentum in a system with respect to time is zero.
thus, my textbook says, the total momentum of that system is constant.

i'd like to understand how one implies the other if anyone could give me a conceptual explanation? i understand the steps to get the derivative of total momentum equation. i just don't have a good grasp on how that implies that the total momentum of the system is constant.

Homework Equations



dP/dt = 0 (where P is a vector quantity and is the total momentum of a system)

The Attempt at a Solution



integrate dP/dt = 0 and you get P = C, a constant. that is one way to get the answer but i am not satisfied. i want a better explanation.
 
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gibberingmouther said:
integrate dP/dt = 0 and you get P = C, a constant. that is one way to get the answer but i am not satisfied. i want a better explanation.
There is no "better" explanation than the explanation. The primitive function of zero is a constant. There is absolutely nothing more to it. The derivative with respect to time equal to zero literally tells you that the function does not change with time.
 
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1. What is a momentum equation?

A momentum equation is a mathematical representation of the relationship between an object's mass, velocity, and force. It is used to analyze the motion of objects and predict their future behavior.

2. Why is understanding the implications of a momentum equation important?

Understanding the implications of a momentum equation is important because it allows us to make accurate predictions about the motion of objects and the forces acting upon them. This knowledge is crucial in fields such as physics, engineering, and mechanics.

3. How is momentum related to Newton's laws of motion?

Momentum is closely related to Newton's laws of motion. The first law states that an object will remain at rest or in uniform motion unless acted upon by an external force. The second law states that the force applied to an object is proportional to its mass and acceleration, which is mathematically represented by the momentum equation.

4. Can momentum be conserved?

Yes, momentum can be conserved. According to the law of conservation of momentum, the total momentum of a closed system remains constant in the absence of external forces. This means that the total momentum of all objects before a collision or interaction is equal to the total momentum after the event.

5. How is a momentum equation applied in real-life situations?

A momentum equation can be applied in various real-life situations, such as predicting the trajectory of a projectile, analyzing the motion of vehicles in traffic, and understanding the behavior of fluids in pipes. It is also used in the design of structures and machines to ensure their stability and safety.

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