Cross Post from Classical Physics: Calculus in Impulse Momentum Theorem

In summary, the conversation involves the poster apologizing for any mistakes in their first post and asking two questions. The first question is about finding a tutorial for using embedded LaTex and the second question is about understanding the calculus behind the impulse momentum theorem. They mention needing help with the integral calculus and ask for guidance.
  • #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
Well, there's a dedicated thread on PF which explains you how to use LaTex.

As for the

[tex] I= \int\limits_{t_1}^{t_2} \frac{dp}{dt} \, dt =... [/tex]

Just apply the fundamental theorem of calculus. What's the antiderivative of the integrand equal to ?
 

What is the Impulse Momentum Theorem?

The Impulse Momentum Theorem states that the change in an object's momentum is equal to the impulse applied to it. In simpler terms, it relates the force applied to an object over a period of time to the resulting change in its velocity.

How is calculus used in the Impulse Momentum Theorem?

Calculus is used in the Impulse Momentum Theorem to calculate the integral of the force over time, which gives the total impulse applied to an object. This integral is then used to determine the change in momentum of the object.

What is the significance of the Impulse Momentum Theorem in classical physics?

The Impulse Momentum Theorem is a fundamental principle in classical physics that helps us understand the relationship between forces and changes in an object's motion. It is used in many areas of physics, such as mechanics and thermodynamics, to analyze and predict the behavior of objects.

Can the Impulse Momentum Theorem be applied to real-life situations?

Yes, the Impulse Momentum Theorem can be applied to real-life situations. For example, it can be used to calculate the force required to stop a moving car in a certain distance or to determine the amount of force needed to launch a rocket into space.

How is the Impulse Momentum Theorem related to Newton's Laws of Motion?

The Impulse Momentum Theorem is closely related to Newton's Laws of Motion, particularly the Second Law which states that the net force on an object is equal to its mass times its acceleration. The Impulse Momentum Theorem expands on this concept by taking into account the duration of the force and the resulting change in momentum.

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