Calculus in Impulse Momentum Theorem

In summary, the conversation is about using embedded LaTex and understanding the calculus behind the impulse momentum theorem. The speaker is looking for a tutorial on embedded LaTex and for someone to explain how the equation simplifies to p2-p1. The other speaker suggests that the fundamental theorem of calculus explains this simplification.
  • #1
elementbrdr
43
0
Hi,

This is my first post. Sorry for the mistakes it certainly contains.

I have two questions. First, is there a tutorial for using embedded LaTex? I found some general tutorials on LaTex, but I couldn't get some of the commands listed in that tutorial to work in the embedded LaTex code block. Second, can someone explain the calculus behind the impulse momentum theorem to me? I understand how to get to I = integral{t1 to t2} dp/dt dt. But I don't understand how that simplifies to p2 - p1. I probably just need to brush up on my integral calculus a bit, but I would appreciate it if someone could point me in the right direction.

Thanks!
 
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  • #2
It goes like this:
[tex]I=\int_{t_1}^{t_2}F dt =\int_{t_1}^{t_2}\frac{dp}{dt} dt=\int_{t_1}^{t_2}dp=p(t_2)-p(t_1)=p_2-p_1[/tex]
 
  • #3
elementbrdr said:
I understand how to get to I = integral{t1 to t2} dp/dt dt. But I don't understand how that simplifies to p2 - p1.

This is exactly the fundamental theorem of calculus--an important thing to make sure you understand well.
 

1. What is the Impulse Momentum Theorem?

The Impulse Momentum Theorem is a fundamental concept in physics and mathematics that relates the change in an object's momentum to the impulse applied to it. It states that the impulse (force multiplied by time) acting on an object is equal to the change in momentum of that object.

2. How is calculus used in the Impulse Momentum Theorem?

Calculus is used in the Impulse Momentum Theorem to calculate the exact values of impulse and momentum. By using calculus, we can determine the exact change in an object's momentum over a specific period of time, which is crucial in understanding and applying the theorem.

3. What is the importance of the Impulse Momentum Theorem in physics?

The Impulse Momentum Theorem is essential in physics as it helps us understand the relationship between force, time, and momentum. It is also used to analyze the motion of objects and predict their behavior in collisions or other situations involving changing momentum.

4. Can the Impulse Momentum Theorem be applied in real-life scenarios?

Yes, the Impulse Momentum Theorem is widely used in various real-life scenarios, such as car accidents, sports, and rocket propulsion systems. It is especially crucial in analyzing and preventing collisions and predicting the outcome of a collision.

5. How does the Impulse Momentum Theorem relate to other laws of physics?

The Impulse Momentum Theorem is closely related to Newton's laws of motion, specifically the second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. The Impulse Momentum Theorem helps us understand how the force acting on an object over a certain period of time affects its momentum, which is a crucial aspect of Newton's second law.

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